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even though I've done a lot of work to reinforce the shape of the bodice on spirals, I know I'm going to need to have this additional piece to hold it up as a solid piece: I traced the shape based on where it needs to sit and pre-punched holes to make attaching it easier.

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I have these all saved, and have a set of of favorites I've been working with in a digital collage style (I'll add updates when they're more done)

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I put in (what should be) the final order of supplies and materials I need to get everything done on 4/1, and they should get here on 4/9? I'm waiting for all these odds and ends to show up (and it feels like things are starting to wrap up which is both exciting and stressful!)

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it's 97% done, I finished the last strip and attaching it the week after the shoot (I somehow didn't take any photos of it complete), I just fucked up putting in the zipper and have to quickly redo it.

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it shocks me how quick it's been to construct this so far, since I'm so used to tricky lines and hard materials straight seams on simple fabric is soooo straightforward it blows me away. Everything's basically together: I'm waiting on an order of interfacing to arrive so I can reinforce the mobius of the corset and the hem of the skirt, after that's done it's just a few hours work of finishing edges and attaching everything

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I've been working on spirit, I have everything cut and constructed, and reinforced the base of the corset with twill tape and interfacing to help it hold its shape better

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I've been working on this cuff on and off, I think it's made me bleed more than any other item

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soooo the prototype of these shoes fell apart at the photoshoot, I re-cemented the bases and redraped the shape: instead of having black reinforcements at the sides I've replaced them with PVC strips, and there will be elastic in not only the top band, but at intervals down the leg to keep their shape. just waiting on elastic to arrive

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my ears aren't pierced, so I asked my friend evelyn to try on the earrings I've been working on: mirrors on the left, and optical illusion grid on the right

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I got the veil fabric in a little while ago, on monday I worked on matching up the pattern and creating a 5 yd french seam to make the largest yardage possible-- I've been playing around with the seam placement, because my original measurement plan/draft had it falling over center front for that to be the longest diameter of the oval (on the left). I know putting a seam over the face is a bad idea, so I wanted to see what difference it would make to have the seams line up with the shoulders (on the right). I like it better with the horizontal orientation, but it means that the shorter side of the oval falls over cf, which would reveal the last 10 inches or so of the skirt.

so I'm going to wait to cut this, especially since I've been thinking about moving it around to a different look and that would affect the length. at least I've gotten the hardest part done now, it's mostly cutting and perling from here

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the state of this for the photoshoot, got 4/5 strips attached-- need to stitch one more and attach it and add zipper. I've been working on this nonSTOP since thursday and it's so close to being done

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since I've got about 25 hours of work left to do on this before it's done, there's no way I can finish this for the photoshoot on Sunday-- it's dependent on being on my home form, so I can't work on it at school, which means I only have friday afternoon and saturday to work on it. I'll probably get really close to finishing it by sunday, but it wouldn't be wearable at that point (no zipper, full of pins, just uncomfy for the model)

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getting the strips shaped and lined up properly is taking longer than expected-- I've only got the first strip attached right now with the second pinned, and it takes about the same amount of time to attach as it does to stitch the strip. I'm estimating I've got about 25 hours left of work before this is finished

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I've started shaping and attaching strips to the base (I still have 1.5 strips to stitch but I felt like I needed to start putting them on ASAP)

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To-do list as of end of spring break (3/14)

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To-do list as of end of spring break (3/14)

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I've spent a ton of time getting these ready, from thrifting for the bases to cutting them up to stitching 200" for the strips (plus I was able to use all scrap fabric and mesh!): all that's left to do is pleat a bit of fabric for the band, drape the strips around the legs, and add a closure

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I've got most of my accessories prepped: pvc is cut, I've got all the o-rings and notions (and backups) needed, I'm just waiting on the spheres and screw rivets before assembling, I've got all the jump rings and earring wires I'll need (and backups), I've got the chain needed for the mirror "purse", just waiting on the mirrored acrylic and to laser cut, and I have the mesh bases of the penrose bracelet, slanted lines cuff, and juraj earrings cut- still have to cut the impossible earring bases, and cut and stitch fabric to these bases.

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Finished the earrings that go with look 2, I can still shorten the chain if I like

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I finished adjusting the fit and adding boning for support to spirals, now it's ready for strips to be pinned to place-- I have to add the zipper and finish the back last so I can get it on and off the form

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I've been trying to prep my materials as they come in so that I can assemble as quickly as possible, but as a result most things are are in varying stages of completion. Right now several things are delayed because supplies are coming from overseas, especially the stainless steel spheres that are so integral to the styling of the first 2 looks. So not all the styling will be done for the shoot, but at least I'll have a smattering of small pieces to show

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the masks I designed came in, I've got them all pleated and prepped, with 2/6 shaped with straps-- I'm glad I'll have these ready for the shoot, I'm really pleased with how well they came out!

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both my test prints came in, and thankfully both came out perfectly! I tried taking a small video of them together to demonstrate the optical illusion effect I was hoping for-- I've now ordered the necessary yardages for both prints, they should get here the last week of March

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A big part of why the ordering process took so long was checking my math and making sure I would have enough material: on this page you can see my math for figuring out the yardages for the custom fabrics (alongside some notes on further simplifying)

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After getting that sweet grant check from Massart, I've been ordering all the materials I need for the accessories and the custom printed fabric I'll need: I focused more on the pieces for the first 3 looks in hopes I could get some accessories done for the shoot on 3/20

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I've been working as much as possible on getting the strips done for spirals (I'm getting faster, and I'm about halfway through!), this is what the black side looks like, see picture to right for white side of same strip

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I decided to make crossroads in the same way I made forks (make base, attach strips through slip stitch instead of seaming), so I consolidated my patterns to ignore the slits I'd made before: went from 15 pattern pieces to 4!

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draped the skirt for spirit on 3/2, I draped it inside out (it's easier for me to control darts that way), which is why the godets are concave-- I turned it right side out for the crit on 3/3, and the godets worked like they should

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I'm going to make crossroads instead of intersects: some of the accessories might be shopped around or simplified (like how I'm cutting the earring shapes from mirrored acryllic), and I'll keep updating those changes here

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Made the base on the 27th, I have to (of course) make some fit adjustments, but I'll wait until I get it on the school form. I will probably end up adding some boning around the bodice for support and retaining shape too.

I also finished tracing all the muslin guides on Saturday, ready to start quilting, which I'll do as much as possible until thursday

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Next step is going back and forth between illustrating and drawing on the form to make the color blocked sections

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SORRY for the noises (this is the reality of the radiators in fibers)

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I've finished draping the paper strips for intersects, I think it's done but I think I'll end up futzing with it a little

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my new gold thread came in today, it's exactly what I was looking for! It's quite shiny, and while it snaps sorta easily I can work around that. This spool was a small sample, I'm going to order more as soon as I can, and start quilting the grid with the pieces of muslin I've got traced. (I've got the 2 faces of one final strip left to trace)

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I restarted intersects to be able to make a simpler shape, NOT done yet, just wanted to show process of early steps

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Actually might need to add seams around "cup lines" on bodice

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Actually might need to add seams around "cup lines" on bodice

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I've been staring at this during insomnia hours, and I think I WILL need to add seamlines at least at the 1/2 way horizontal line of the breast (about where I added little panels).

just not sure if i should add seam lines at the underboob line to make a fully formed cup for the corset? I don't really love the look of corsets with cups, and the dart along the princess line might give enough shaping but not too much?

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I FINALLY got it to be perfectly seamless!!
I've been looking at fabric options on spoonflower, I liked the flowiness of the crepe de chine but suspect i'd need something sturdier like a twill to make a substantial corset, so I think i'll settle in the middle with a cotton sateen-- I've actually worked with the sateen before, and I think the sheen of the fabric before it's washed will complement this design nicely.

once i've draped the skirt and traced my patterns, I'll be able to figure out how much yardage I'll need and order it!

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Still have to re-illustrate intersections after I've finished re-sculpting the strips. Until crossroads is completed, "Spirit" will act as the closer for the show, and use most of the styling elements crossroads would have used.

It's kinda hard to say which piece lines up with each "look" for deadlines sake. I'm trying to juggle all of them at once right now, just doing what I can on each at all times. This week (2/21-26) I'm draping and drafting spirit, re-sculpting intersects, and redoing a little prep for spirals. I have to wait for gold thread to arrive before I can work on quilting and I've got to resolve the shapes before I can draft the other two looks, so I've been splitting my time between spirit at home and intersects at school. In the background I've been doing the prep for spirals and some of the accessories I can make out of mesh.

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Veil Print pattern (transparent, organza)

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Veil Print pattern (transparent, organza)

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I'll layer this print over the print with white paths. The dark paths on white background is the starkest effect when transparent.

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Final colorway for base garment (opaque)

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Final colorway for base garment (opaque)

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I can NOT get this pattern to stop showing tile boundaries and I do NOT KNOW WHYYY Ive tried everything!! it seems like a small detail at this scale, but when it's fully printed if you can see the edges it'll ruin the effect of the maze. this problem only shows up so obviously in this colorway, which is baffling

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this should be straightforward to make (I have everything marked and traced and can use this as a draft), with corset construction on the front, grommets hidden beneath the fold of the strip at the back to make a lace-up closure, and I'll add some light interfacing to the strip to make sure it keeps shape. I do want this to be quite flowy, as it'll be under the printed veil, I'd like to see the strip at the back and sides float and flow with movement (opposite of mesh strips that are solid).

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I want to drape the skirt at school to make sure the height is correct, so I was playing around with draping pieces of muslin to make the bodice, and I ended up with a shape I really like (and is actually a mobius strip!). I was working with small pieces to make a composite shape, so ignore the seam lines where I attached a panel. This will actually all be one double-sided piece, getting all the shaping from darts and not seams.

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I realized I never put my final moodboard in here? Referencing this as I drape the "Spirit of the Labyrinth" piece

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I like this MUCH better than the first version, I'll just be playing around with color ways now. Only took about 10 hours to make this start to finish!

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I've been brainstorming AGAIN on how to simplify, I had the idea to use digital printing instead of handworking, and then tried to figure out where I can apply it to save time. I think what I'll do is bookmark crossroads until after the semester, and make a bare-minimum cut-and-sew look with the digital print. I was thinking back on old ideas I didn't get to use, I thought a sheer veil with printed mazes surrounding them to the floor, and veils are so simple to make that it shouldn't take too much time at all.

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I really like making repeat patterns, they come pretty naturally to me, and they work well with the labyrinth

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I've been thinking about, as a compromise, to use digital printing for a look instead of handwork. This took less than 4 hours to make, I drew it by hand and then finessed the details in illustrator. I like this but it's not quite what I had in mind, I just want to play around with tile size and path width, I'd like it to look a little more ordered

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this was sorta squeezed into a sketchbook page with other stuff

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I've decided to bring the gold thread idea back in (I've already been looking for a better, more metallic thread) in the edited version of loops. These sketches were how I worked out the idea of what I wanted to do, the 3 sketches on the bottom left are what I plan to do

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was testing out the curve of the mesh, and the type of path I have here is not working the best it could with the mesh. It's also killing me how empty it is, I've sat down and brainstormed a bunch of way to improve this

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I've been trying to make up a little time on loops, I've gotten about 8 hrs of quilting done so far. Something has felt off about this for awhile, and not only is the scale of stitches wrong, the dynamic areas of the design are being swallowed up by the curve. I NEED to redesign the surface pattern, at least I've only started one piece

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*updated to reflect replacing crossroads with spirit of laby

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I'm working on the styling for the collection, and the first step in picturing that is figuring out the makeup. I started with this before making the padlet

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I started quilting Loops on the 1st, I was able to get this much done over the past few days (covid exhaustion has knocked me out and killed my focus), but I'm already feeling kinda meh about this. The scale of the grid feels too big, and the basic black on white feels too straightforward. hmmm

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Based on a suggestion at reviews, I wanted to play around with gold thread and see what the visual effect would be. I think it's interesting but not quite usable for this: I wouldn't be able to use the gold against a white background in the same way, wouldn't be able to alternate colors, I don't like how gold thread just ends up being yellow and has no luster

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I got the lining in, hammered in 38 grommets, and covered the edges with black trim. I think this black trim had a great effect in defining the shape, and I think the corset closure is a nice detail on the back. It kept shrinking with each thing I did, which is why the closure goes down so low. I tried the best I could on the craft of the finishing elements, but the bad craft on the rest is killing me. I'm just glad I can put it down now, I want it known I'm not proud of it.

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“Everything has its pattern,” Freddy put in. “If you find it, the great can be contained within the small.”

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I've finished the edges of all the white sections, adjusted the dart on the front left, re-added the kick-pleat, and finished the edges of the placket in the back. Next steps is interfacing a few black sections that are sagging, adding the lining, and binding the edges of neckline and hem with twill tape.

I've been thinking a lot about the closure: the mesh is so stiff that you really have to pull the back shut, even though there's plenty of room at the hips for it to come back there's just no stretch. I was originally planning to just put a zipper in at the back, but I don't think that would hold up with the amount of pulling. I've decided instead to add grommets and make it a lace-up closure, which should work much better with the pulling of the mesh. I have to wait until the lining is in to add these.

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I adjusted the patterns based on the new fit (thankfully most of the darts were uninterrupted by seams, so making the changes was easier than expected)

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Forks is finally done!!
you can see in this video there were a few pins where I had some stitching to do after getting it off the form, which is all finished now (getting it on and off the form is a bit of an endeavor, but it'll be easier for a model to put it on and off because they can bend their knees)

it took 51 hours in total to make this piece, and I figure materials were $160 (I used 2 rolls of mesh at $70 each, findings/notions and the 1 1/2 yards of fabric make up the other $20)

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I've got loops back on the form so I can adjust the fit-- the back fits fine, so I've extended and widened the darts along the princess line and the bust dart. Now that I know the changes to make, I can alter my patterns

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Written description of the different facets of the project:
I've been struggling to describe everything involved in what I plan to do, and this draft was an attempt to begin to organize those thoughts

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Most of the caps are attached (I stitched two pieces on the wrong face)-- covering up the negative spaces and hiding the structure within already makes such a difference on the silhouette

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detail shot of the attached cap for forks, this is one of 8, I only have 2 left to do

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general sketches of the idea I had for the shoes to go with forks, I would sculpt double sided strips around the leg form, and support the shape with a garter belt closure above the knee.

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I've been thinking about different names for the pieces, in my fibers review it was suggested that the word "look" doesn't sum up everything involved. Since each look is an evolution of a larger process and each look is an evolution on its own, I've been thinking about calling them "phases" instead. So parallels would be phase one, forks phase two, loops phase three, etc.. This works with how I've been thinking of the first two garments as prototypes, as early phases in their evolution since I know I can do better on them without throwing away the work I've done already. It also makes me feel better to think of all pieces as phases and part of an evolution, since it takes the pressure off me to create a perfect final version on the first try.

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Since I want to remake parallels anyways, I've been wondering if it would be more successful if it was monochrome like forks. I had originally planned for both of the first two prototypes to be monochromatic so they could walk together, but I think the graphic quality of the path against the body is lost in this version

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I finished attaching the strips to the base and marked out the places caps will go with blue thread to help in drafting. I still have a few areas of stitching to do that require the dress being off the form, including the darts that need to be taken in on the right side. I also have to add the snaps and a hook and eye above the zipper (I lost mine and had to order more).

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I planned this out based on rough estimations of how long I think each item on my to-do list will take: I don't expect to follow this schedule to the letter but it was more of an attempt to see how long things could take and if it would fit into the semester.

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traditional sketchbook pages and 2d work, companion to this padlet

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I already have a website, which was one of my big projects during my leave, and so I've been updating my site through an "In Process" page. I don't like to share larger projects like this collection until they're done, but this page is proving to be a good way to provide a different perspective of my process and keep people updated. Eventually my thesis collection and all it encompasses will have its own page on my site, but seeing as how this project won't be done until the Fall, these updates will have to do

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I'm not as happy with how this video turned out, but I learn best by doing and I have a lot of ideas of how to improve this idea-- I've been collecting a lot of inspirations for documentation in my "Install/Exhbit ideas" padlet (which has been my primary place to put new ideas, this padlet has transitioned into mostly process updates)

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documentation of the version of the booklet seen at reviews-- a few edits and updates will be made when everything is finished, but I've been reteaching myself video editing so that I can better document my work

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I feel like I've mentioned a million times that I've been drawing these mazes for years, BUT the real story is that I began drawing in this more fluid style my sophomore year-- I was in Creative 1 at the time, and I wanted to incorporate the mazes into my geometric design and it just didn't work out. When me and Sara were talking about my plans and how I was disappointed to not be able to figure out how to incorporate the mazes, Sara suggested I research Shipibo textiles because my designs reminded her of their geometric style-- and most importantly, told me to keep developing and making these mazes until I could figure it out for use in a later project because they were really exciting. And that's exactly what I did, bookmarking this idea through my junior year and my LOA as I gathered more techniques and knowledge, so it was such a nice full circle moment for Sara to suggest Shipobo-Konibo textiles again and remember that conversation :)

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Northern Peru & Amazonia Tours | Kuelap & Gocta | Amazon River Cruises & Lodges

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Shipibo-Konibo is an indigenous Amazonian culture, most numerous in Peru's Ucayali Department.

Renowned for distinctive geometrically-decorated textiles created by women.

We examine the process behind this intricate art form.

Many theories abound as to the meaning of the Shipibo-Konibo's broad and thin, angular, geometric patterns.

Some believe it to represent a stylised language; a mapping of the rivers in Amazonia; a representation of the spiritual word; or the shape of the Anaconda.

Others state that these designs describe the lives of their families and communities in the rainforest.

Although it is difficult to attribute one meaning to the designs, their value and uniqueness is indisputable.

In the Shipibo-Konibo language, Chono Shobo means 'The House of the Hummingbird', and is the name of a centre in Pucallpa where women of the community gather to work on their handicrafts.

Here the elders pass their ancestral techniques to younger generations. Note that it is exclusively women who are involved in the manufacture of the textiles.

Some novice design makers start learning this art as early as the age of five. These secrets will guide them through the rest of their lives, shaping their designs while hand dying and painting, embroidering or weaving.

The geometrical designs are called quene or kené, literally 'symbols of ethnic identity'. Indeed, they have always been a symbol of Shipibo-Konibo identity, differentiating them from other indigenous groups.

The elaborate geometrical figures symbolise the ethnic group's cosmos and mythology.

Ronin is 'The Great Boa' who brought the universe into existence, and has a particular kené, that represents the patterns on her skin.

Ronin's skin is said to contain all of the design patterns found in the natural world, such as the fur of the jaguar, the wings of a butterfly or the surface of a leaf. Every human, animal and plant is said to have a unique design.

The hallucinogenic vine, ayahuasca, is a key element in Shipibo-Konibo culture, and often used to facilitate the recognition of these designs in the world around them.

It is through these visions that the women begin the process of creating the distinct hand-painted textiles.

Moreover, there are melodies and chants ( huehua) that serve as codes to each design, and relate to shamanic visions experienced under the influence of ayahuasca.

Therefore, Ronin kené huehua, means literally 'the song of the design of the Great Boa', and has a place of great importance in both Shipibo-Konibo cosmology and their artwork.

The Shipibo-Konibo paint on large sheets of pure cotton muslin, which are cut into smaller sections, before beginning the dying process.

Women often work together painting on the same sheet at the same time, coordinating designs by observing the other's progress.

One of the most difficult tasks is drawing the first line on a virgin cloth.

The painter has to approach this task with extreme delicacy: if only one drop of colour stains the sheet, all preceding work will be in vain, because the stain can never be washed off again.

Women often paint all day and night to finish their work in time. Younger girls may be employed to fill the spaces between the bold lines with delicate filling patterns.

The dyes used to create the colours come from a variety of organic materials found in the Amazon rain forest, such as the bark of the mahogany tree, Huito fruit ( Genipa americana) or a mud collected from the bottom of ponds or streams.

They can be difficult to handle because of their pasty consistency.

For the black-on-rust designs, they dye the entire fabric with the plant-based brown tint, and then paint on it with mud, thus turning only those painted portions to black.

Hand-painted textiles might be dyed up to ten times and then be left to dry in the strong Amazon sunlight. Then they are hand-painted using very fine sticks, before being dried in the sun again, and finally washed.

For black-on-white cotton designs, they paint onto natural, un-dyed muslin with a brown dye, and then bathe the entire fabric in mud, thus turning the painted portions to black.

Even if the meaning of the Shipibo-Konibo designs is not apparent, visitors appreciate the beautiful patterns, the soft curves and pristine, yet authentic look.

By purchasing these hand-painted textiles, they are helping the Shipibo-Konibo preserve their culture and maintain economic stability and self-sufficiency.
A word of warning: on account of the organic nature of the materials used, it is crucial that original Shipibo-Konibo textiles are handled and washed with care. Be sure to add half a cup of salt to each load of washing, in order to keep the natural dyes from bleeding.

Source: http://songoftheamazon.com/shipibo-art-kene/

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Art of Shipibo-Konibo | Meaning & Process of Geometrical Textile Designs | Pucallpa, Ucayali, Peru - Northern Peru & Amazonia Tours | Kuelap & Gocta | Amazon River Cruises & Lodges

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PeruNorth's investigation of the art of Shipibo-Konibo, an indigenous Amazonian people found in greatest numbers around Pucallpa, Department of Ucayali. Striking geometrical textile designs are mysterious, but reflect belief system, which is influenced by ayahuasca experience. Elaborate process whereby women dye, cut & decorate muslin. Knowledge passed to next generation.

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I was also told to look into Klein Bottles, which are very interesting to me shape wise, but I think they may be a step too complicated for this project and too similar to the mobius for another project?

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In topology, a branch of mathematics, the Klein bottle () is an example of a non-orientable surface; it is a two-dimensional manifold against which a system for determining a normal vector cannot be consistently defined. Informally, it is a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down. Other related non-orientable objects include the Möbius strip and the real projective plane. Whereas a Möbius strip is a surface with boundary, a Klein bottle has no boundary (for comparison, a sphere is an orientable surface with no boundary).

The Klein bottle was first described in 1882 by the German mathematician Felix Klein. It may have been originally named the Kleinsche Fläche ("Klein surface") and then misinterpreted as Kleinsche Flasche ("Klein bottle"), which ultimately may have led to the adoption of this term in the German language as well.

The following square is a fundamental polygon of the Klein bottle. The idea is to 'glue' together the corresponding coloured edges with the arrows matching, as in the diagrams below. Note that this is an "abstract" gluing in the sense that trying to realize this in three dimensions results in a self-intersecting Klein bottle.

To construct the Klein bottle, glue the red arrows of the square together (left and right sides), resulting in a cylinder. To glue the ends of the cylinder together so that the arrows on the circles match, one would pass one end through the side of the cylinder. This creates a circle of self-intersection - this is an immersion of the Klein bottle in three dimensions.

This immersion is useful for visualizing many properties of the Klein bottle. For example, the Klein bottle has no boundary, where the surface stops abruptly, and it is non-orientable, as reflected in the one-sidedness of the immersion.

The common physical model of a Klein bottle is a similar construction. The Science Museum in London has a collection of hand-blown glass Klein bottles on display, exhibiting many variations on this topological theme. The bottles date from 1995 and were made for the museum by Alan Bennett.

The Klein bottle, proper, does not self-intersect. Nonetheless, there is a way to visualize the Klein bottle as being contained in four dimensions. By adding a fourth dimension to the three-dimensional space, the self-intersection can be eliminated. Gently push a piece of the tube containing the intersection along the fourth dimension, out of the original three-dimensional space. A useful analogy is to consider a self-intersecting curve on the plane; self-intersections can be eliminated by lifting one strand off the plane.

Suppose for clarification that we adopt time as that fourth dimension. Consider how the figure could be constructed in xyzt-space. The accompanying illustration ("Time evolution...") shows one useful evolution of the figure. At t = 0 the wall sprouts from a bud somewhere near the "intersection" point. After the figure has grown for a while, the earliest section of the wall begins to recede, disappearing like the Cheshire Cat but leaving its ever-expanding smile behind. By the time the growth front gets to where the bud had been, there's nothing there to intersect and the growth completes without piercing existing structure. The 4-figure as defined cannot exist in 3-space but is easily understood in 4-space.

More formally, the Klein bottle is the 0 ≤ 0 ≤ quotient space described as the square [0,1] × [0,1] with sides identified by the relations for y ≤ 1 and for x ≤ 1.

Like the Möbius strip, the Klein bottle is a two-dimensional manifold which is not orientable. Unlike the Möbius strip, the Klein bottle is a closed manifold, meaning it is a compact manifold without boundary. While the Möbius strip can be embedded in three-dimensional Euclidean space R 3, the Klein bottle cannot. It can be embedded in R 4, however.

The Klein bottle can be seen as a fiber bundle over the circle S 1, with fibre S 1, as follows: one takes the square (modulo the edge identifying equivalence relation) from above to be E, the total space, while the base space B is given by the unit interval in y, modulo 1~0. The projection π: E→ B is then given by .

The Klein bottle can be constructed (in a four dimensional space, because in three dimensional space it cannot be done without allowing the surface to intersect itself) by joining the edges of two Möbius strips together, as described in the following limerick by Leo Moser:

A mathematician named Klein
Thought the Möbius band was divine.
Said he: "If you glue
The edges of two,
You'll get a weird bottle like mine."

There is a 2-1 covering map from the torus to the Klein bottle, because two copies of the fundamental region of the Klein bottle, one being placed next to the mirror image of the other, yield a fundamental region of the torus. The universal cover of both the torus and the Klein bottle is the plane R 2.

The fundamental group of the Klein bottle can be determined as the group of deck transformations of the universal cover and has the presentation .

Six colors suffice to color any map on the surface of a Klein bottle; this is the only exception to the Heawood conjecture, a generalization of the four color theorem, which would require seven.

A Klein bottle is homeomorphic to the connected sum of two projective planes. It is also homeomorphic to a sphere plus two cross caps.

When embedded in Euclidean space, the Klein bottle is one-sided. However, there are other topological 3-spaces, and in some of the non-orientable examples a Klein bottle can be embedded such that it is two-sided, though due to the nature of the space it remains non-orientable.

Dissecting a Klein bottle into halves along its plane of symmetry results in two mirror image Möbius strips, i.e. one with a left-handed half-twist and the other with a right-handed half-twist (one of these is pictured on the right). Remember that the intersection pictured is not really there.

One description of the types of simple-closed curves that may appear on the surface of the Klein bottle is given by the use of the first homology group of the Klein bottle calculated with integer coefficients. This group is isomorphic to Z× Z 2. Up to reversal of orientation, the only homology classes which contain simple-closed curves are as follows: (0,0), (1,0), (1,1), (2,0), (0,1). Up to reversal of the orientation of a simple closed curve, if it lies within one of the two crosscaps that make up the Klein bottle, then it is in homology class (1,0) or (1,1); if it cuts the Klein bottle into two Möbius strips, then it is in homology class (2,0); if it cuts the Klein bottle into an annulus, then it is in homology class (0,1); and if bounds a disk, then it is in homology class (0,0).

To make the "figure 8" or "bagel" immersion of the Klein bottle, one can start with a Möbius strip and curl it to bring the edge to the midline; since there is only one edge, it will meet itself there, passing through the midline. It has a particularly simple parametrization as a "figure-8" torus with a half-twist:

In this immersion, the self-intersection circle (where sin( v) is zero) is a geometric circle in the xy plane. The positive constant r is the radius of this circle. The parameter θ gives the angle in the xy plane as well as the rotation of the figure 8, and v specifies the position around the 8-shaped cross section. With the above parametrization the cross section is a 2:1 Lissajous curve.

A non-intersecting 4-D parametrization can be modeled after that of the flat torus:

where R and P are constants that determine aspect ratio, θ and v are similar to as defined above. v determines the position around the figure-8 as well as the position in the x-y plane. θ determines the rotational angle of the figure-8 as well and the position around the z-w plane. ε is any small constant and ε sin v is a small v depended bump in z-w space to avoid self intersection. The v bump causes the self intersecting 2-D/planar figure-8 to spread out into a 3-D stylized "potato chip" or saddle shape in the x-y-w and x-y-z space viewed edge on. When ε=0 the self intersection is a circle in the z-w plane <0, 0, cos θ, sin θ>.

3D pinched torus / 4D Möbius tube

The pinched torus is perhaps the simplest parametrization of the klein bottle in both three and four dimensions. It's a torus that, in three dimensions, flattens and passes through itself on one side. Unfortunately, in three dimensions this parametrization has two pinch points, which makes it undesirable for some applications. In four dimensions the z amplitude rotates into the w amplitude and there are no self intersections or pinch points.

One can view this as a tube or cylinder that wraps around, as in a torus, but its circular cross section flips over in four dimensions, presenting its "backside" as it reconnects, just as a Möbius strip cross section rotates before it reconnects. The 3D orthogonal projection of this is the pinched torus shown above. Just as a Möbius strip is a subset of a solid torus, the Möbius tube is a subset of a toroidally closed spherinder (solid spheritorus).

The parametrization of the 3-dimensional immersion of the bottle itself is much more complicated.

Regular 3D embeddings of the Klein bottle fall into three regular homotopy classes (four if one paints them). The three are represented by

The "traditional" Klein bottle

Left handed figure-8 Klein bottle

Right handed figure-8 Klein bottle

The traditional Klein bottle embedding is achiral. The figure-8 embedding is chiral (the pinched torus embedding above is not regular as it has pinch points so it's not relevant in this section). The three embeddings above cannot be smoothly transformed into each other in three dimensions. If the traditional Klein bottle is cut lengthwise it deconstructs into two, oppositely chiral Möbius strips.

If a left handed figure-8 Klein bottle is cut it deconstructs into two left handed Möbius strips, and similarly for the right handed figure-8 Klein bottle.

If the traditional Klein bottle is two color painted, this induces chirality on it, creating four homotopy classes.

The generalization of the Klein bottle to higher genus is given in the article on the fundamental polygon.

In another order of ideas, constructing 3-manifolds, it is known that a solid Klein bottle is homeomorphic to the Cartesian product of a Möbius strip and a closed interval. The solid Klein bottle is the non-orientable version of the solid torus, equivalent to

A Klein surface is, as for Riemann surfaces, a surface with an atlas allowing the transition maps to be composed using complex conjugation. One can obtain the so-called dianalytic structure of the space.

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In topology, a branch of mathematics, the Klein bottle () is an example of a non-orientable surface; it is a two-dimensional manifold against which a system for determining a normal vector cannot be consistently defined. Informally, it is a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down.

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A suggestion from fashion reviews on inspiration on how to use technology to increase interaction with the pieces (also just a great list of some of my favorite designers)-- with special attention paid to Viktoria Modesta's "Prototype" video as a way of documenting my work through film

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10 (Literally) Bright, Shiny, Splashy Pieces from #Techstyle

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Updated plans for parallels and forks 1/9

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Updated plans for parallels and forks 1/9

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I've been looking over what I need to do to finish the first two prototype looks: I think the only way I'll be happy with parallels is to remake it (the choice of voile and the rush job means the craft is just at a point of no return), and I think I could do a better job on forks (the silhouette is just small and  not as sculptural as I'd like)

I don't want to do any more work on parallels because it would be a waste of time, I have a better plan for remaking but I worry I won't have time this semester. I'm trying to finish forks to a better point (I may wait to add the caps) so that if I don't decide to remake it I have this as a backup

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I made another padlet to gather my ideas, references, and resources for planning the exhibition style presentation of this project. I'm going to try to plan for the final presentation being in the fall when case numbers have gone down (and this will give me more time to plan and finesse the details of the garments without rush over the summer)

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I have a few small adjustments to make to the base garment to adjust for fit, but I've got the first strip pinned into place and I'm really happy with how the lines are curving

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Since the coverstitch was not working in my favor i switched to my home sewer and I'm much happier with how it turned out: not all the lines are perfect but as a whole it achieves the effect I wanted

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I've drafted and made the base garment complete with boning and zipper, I drafted and cut both mesh and fabric of the strips, and drafted directional lines to orient myself while stitching. I planned to use the coverstitch to cut down on time, but the damn thing came unthreaded so often that it didn't save that much time, and the elastic wooly thread started to peak through to the face of the strip. So I've moved to working from my home sewer for efficiency's sake

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I also sculpted and edited my third look of the semester, which I'm currently in the process of making

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Parallels back on form, after basting, before topstitching

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Parallels back on form, after basting, before topstitching

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I haven't updated in a little while because I've been so busy getting things done: I cut and sculpted the mesh to fit the form, I basted the mesh and voile sections, cut and shaped the black sections (and had to re-do after the mesh shifted), basted and then topstitched all the black sections, and I'm currently in the process in adjusting fit, adding zipper, finishing edges of the voile, and reinforcing the hem and neckline.

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includes all sketchbook pages and 2d development

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-I'm so close to being able to get this done in time, but it all depends on having the mesh to work around. It was supposed to be here on friday the 12th, but fedex delayed the shipment and now it won't get here until the 22nd. I'm SO frustrated that  this is beyond my control
-I'll spend the day thursday finishing up prepping the sections that will be appliquéd (the black sections need fray tack on the notches) so that when the mesh DOES come everything is ready to go

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this is what I have for the base garment right now, I cut the base extra generously around the hem and neckline because I need to shape those areas around the mesh when it's on. Because the measurements of the school's mannequins are different than my home mannequin, I had to pin the negative areas to this base to be sure my drafts of these finicky shapes matched their actual placement on the body.

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all the different components of parallels are drafted, my plan for construction is to cut mesh in that shape, shape and wrap it around the body over the base garment, and then baste the voile overlays to the mesh in the sections marked. I'll then shape the neckline and the hem of the base, and baste the black sections to the garment, take the whole thing to the machine and topstitch the black sections, which will secure all layers.

(also! in terms of function I'm putting in a back zipper, it's marked in the draft. I also edited my sloper to adjust fit, and there is a kick pleat drafted in- the mesh will be basted up to the edge of the pleat on the outer surface, so no mesh is in the pleat, enabling movement.)

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as part of the drafting process I cut the strip out of the dress, keeping the negative areas pinned to the form-- the strip actually lays flat, as you can see above