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Overview

This app generates a range of common polyhedra and lets you apply mathematical operations on them to create some interesting and artistic sculptural forms. I have tried to include most of the standard operations from Conway polyhedron notation - borrowing heavily from some of the techniques used in Anselm Levskaya's polyHédronisme and George Hart's Polyhedron Generator - as well as a couple of my own for spherical inflation and a bit of randomness.

Once you have selected a base polyhedron, you can either enter a notation command string directly, minus the polyhedron identifier at the end, or build one up by adding and editing components in the operator stack immediately below.

Conway Polyhedra Notation

Importantly, you don't need to know anything about Conway polyhedron notation to have fun with this app. You can just experiment by trying out different operators one by one to see what they do. Moreover, you can choose one of the examples and then start enabling/disabling or editing the paramaters in order to experiment.

If you do want to know more, the best place is the Wikipedia page linked to above. Hopefully at some point I will get enough time to go back and write a detailed explanation for each of the operations and what they do, but until then it's up to Wikipedia and George Hart's original explanations.

As notation strings can sometimes get quite complex, especially when using bracketed arguments, I have tried to make the operator stack a bit more approachable by including all the available paramaters as interactive sliders.

To enter a number directly, either click the slider instead of dragging it, or manually edit the appropriate argument in the notation text. By default, the operator stack will update whenever you manually change the notation in the text editor.

Background

I have always wanted to do a WebGL version of the polyhedron viewer I wrote in Processing some years ago, but it was just a folly and there were always higher priorities. However, I recently needed to include some basic polyhedra in my Tree Generator app, so had to convert some of the old code anyway. At the same time I was trying to develop a bullet-proof closed-shell geometry class for my BIM tools and, having seen and been so completely inspired by polyHédronisme, I figured that it might make an excellent visual test suite and provide just the excuse I needed.

Interesting Features

The following are some of this app's features and idiosyncrasies:

Don't go too beserk, but this app will handle higher-order polyhedra with several hundred thousand vertices and a similar number of faces. However, anything above about 200k will start to test your patience when editing it - so best to edit a simplified base and then add smoothing expansions only when you want to export or visualise.

The final generated polyhedra always has a maximum radius of 1 metre. This may mean that some extrusions cause the apparent base polyhedron to shrink in size relative to the external projections, but this is intended behaviour.

I have tried to provide a range of different facet colouring options, based on relative area, number of edges, orientation or a combination of all three to create a signature for like faces. Different types of polyhedra will look good with some and not others, so you will need to experiment for best results.

I have taken some egregious liberties by adding a couple of non-standard operations such as Jitter (J), Wrinkle (W) and Inflate (I)

© Dr. Andrew J. Marsh, 2019.
View Manipulation

You can interactively adjust the 3D view of the model using a mouse, pen or stylus, or by touch on a tablet or phone. You can also use the items in the 3D View Settings popup.

NOTE: You can use the Shift and Ctrl/Meta keys to adjust the increment of each scroll event or key press.

Keyboard Modifiers

The Shift and Ctrl/Meta keys are used pretty extensively to modify interactive data entry. This applies to all increment buttons, scroll wheel motion, slider controls and input elements.

Shift Key:

Increases input to larger values, usually by ten times or significantly larger increments such as 1 month for dates and 1 hour for times.

Ctrl or Meta Key:

Decreases input to smaller values, usually by one tenth or the smallest reasonable increment such as 1 day for dates or 1 minute for times.

NOTE: You can use the scroll wheel to edit a data value when hovering over any slider, numeric input or even table rows that indicate their editibility.

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This app generates a range of common polyhedra and lets you apply mathematical operations on them to create some interesting and artistic sculptural forms. Once you have selected a base polyhedron, you can either enter a notation command string directly, minus the polyhedron identifier at the end, or build one up by adding and editing components in the operator stack immediately below.

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Children should start completing activities with Polyhedrons by the 6th grade.

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Grade 6

A student should be able to do

• Compose polygons from

triangles.

• Decompose polygons into

triangles.