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- Davi Mendes;
- Fernando Gabriel;
- Filipe Campos;
- Italo Santos;
- Leonardo Menezes.

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-> Eles são formas tridimensionais formadas por meio de polígonos e que possuem suas faces planas.
-> A palavra poliedro veio do idioma grego: poly (vários) + hedra (faces). Um sólido geométrico de varias faces

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Pelo fato dos poliedros não possuírem curvas e apenas retas, eles podem ser facilmente planificados. Indo de uma figura 3D para uma 2D.
Este processo de planificação, é bastante utilizado na produção de embalagens poligonais, como por exemplo numa caixa de chocolate. A caixa é imprimida de maneira planificada e depois é "desplanificada".

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-> Os poliedros podem se dividir em dois: poliedros convexos e os côncavos.
- Convexos: Quando qualquer reta que liga dois pontos no poliedro fica completamente inserido dentro dele.
- Côncavo: Quando qualquer reta que liga dois pontos ou mais do poliedro está inserida fora dele.

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Os poliedros regulares possuem todas as suas faces constituídas por polígonos regulares e seus ângulos congruentes.
Há apenas 5 poliedros regulares, o tetraedro, hexaedro, octaedro, dodecaedro e icosaedro

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-> São poliedros de Platão, os poliedros convexos que possuem todas as faces com o mesmo número de arestas e que possuem todas as suas vértices sendo extremidade de uma mesma quantia de arestas.
-> Os 5 poliedros de Platão: tetraedro (4 lados), hexaedro (6 lados),  octaedro (8 lados),  dodecaedro (12 lados) e o icosaedro (20 lados).
-> No livro "Os Elementos" de Euclides, dizia que Platão tinha descoberto esses tipos de poliedros, porém, os pitagóricos e o grego matemático Teeto, já tinham descoberto três deles. Os pitagóricos um e o Teeto dois. Entretanto foi Platão que descobriu que existem apenas 5 tipos de poliedros de Platão.
-> O grego Platão, buscava explicar a origem do universo por meio da matemática, pelos poliedros.

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-> O matemático Leonhard Euler, descobriu em 1758 uma fórmula fundamental para o cálculo da vértice, aresta ou face de qualquer poliedro convexo. O Teorema de Euler, em homenagem ao seu nome, o teorema diz que:
V + F = A  + 2
Onde, V = Nº de vértices, F = Nº de faces e A = Nº de arestas.

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-> A soma dos ângulos da face de um poliedro convexo é medida por meio da seguinte equação:
S = (V-2). 360º
Onde, V = Nº de vértices

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-> No nosso cotidiano os poliedros sempre estão presentes ao nosso redor. Eles são indispensáveis na arquitetura e na construção de edifícios, casas e etc.

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Na natureza alguns minerais e pedras preciosas que são formadas, são poliedros.

Além de que as abelhas constroem favos de formato hexagonal para terem mais espaço para depositarem seu mel.

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Nos videogames e nas animações a utilização de polígonos é é crucial para a criação de modelagem de elementos em 3D. Nesses elementos são colocados milhares de polígonos para que o gráfico seja o melhor possível.

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Acontece que, com o passar do tempo e com a evolução da tecnologia, os videogames passaram a utilizar cada vez mais polígonos como forma de aprimorar seus gráficos.
Como podemos ver nesse exemplo, onde a imagem da esquerda possui mais ou menos 100 polígonos é o da direita 6.000

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Acesse neste link uma pasta com três vídeos de resoluções de problemas poliédricos:
https://drive.google.com/drive/folders/1dhjWqUD09EA4SFywUPtboTXCCxgkzBSR?usp=sharing

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PDF ANEXADO

KAHOOT: https://create.kahoot.it/share/poliedros/9ee6146f-a1be-4be2-9c68-6862ec20c802

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SILVA, Luiz Paulo Moreira. "O que é poliedro?"; Brasil Escola. Disponível em: https://brasilescola.uol.com.br/o-que-e/matematica/o-que-e-poliedro.htm. Acesso em 05 de setembro de 2022.

LUIZ, Robson. "Poliedros"; Brasil Escola. Disponível em: https://brasilescola.uol.com.br/matematica/poliedros.htm. Acesso em 05 de setembro de 2022.

Sólidos de Platão – Derivando a matemática. Disponível em: <http://www.ime.unicamp.br/~apmat/solidos-de-platao/>. Acesso em: 5 set. 2022.
JONES, Chris. - "Eye Piece". Disponível em: <https://www.youtube.com/watch?v=TAZIvyAJfeM>. Acesso em: 7 set. 2022.

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https://www.historydefined.net/what-was-the-purpose-of-a-roman-dodecahedron/

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One of the significant advantages any historian of ancient Rome has is a wealth of written material that has survived from 2,000 years ago to help explain to us what the remains of the Roman Empire mean.

For instance, we know how the towns of Pompeii and Herculaneum ended up buried under volcanic ash because Pliny the Younger wrote about Mount Vesuvius erupting in 79 AD and destroying the two settlements.

Likewise, we know that the giant concrete arches dot Italy and France today's landscapes today because many Roman authors dedicated sections of their work to the discussion of the aqueducts.

Julius Sextus Frontinus, a Roman engineer, even wrote a book called On Aqueducts in the first century AD.

But occasionally, historians are stumped by something from Roman times because there is no obvious answer for what it is, and there is also no documentary material from the time that discusses it. Such is the case with the Roman dodecahedra.

Roman Dodecahedra

Roman Dodecahedron

What are Roman dodecahedra? A dodecahedron is any three-dimensional object with twelve individual flat faces.

In the Roman case, these were small objects, usually measuring between 1.5 and 4.5 inches in diameter, which one could hold in their hands. They were generally cast from metal, typically a copper alloy.

Moreover, the dodecahedra almost always had a large hole in the center of each of the twelve faces. The first such object was discovered in 1739 in France, but many other examples have been found since.

Interestingly, you can't find these all over the former Roman Empire. Instead, you can only find them in Britain, Gaul, Germania, and over into Noricum and Pannonia in what is now Austria and Hungary.

They are most prevalent in Roman Gaul, the region approximating modern-day France, and parts of Belgium and Switzerland.

A smaller number of what are known as icosahedra have also been discovered. These are three-dimensional objects with twenty individual flat faces on them. They exist in far smaller numbers.

Typically, all of the dodecahedra and icosahedra, which are extant today, date to the later imperial period, i.e., between the late second and fourth centuries AD.

Two dodecahedra and an icosahedron. Rheinisches Landesmuseum Bonn, Germany. CC BY-SA 4.0

A Device for Studying Coins?

Because we have no written records to work from and there is no obvious answer to explain the function of a dodecahedron, historians and archaeologists have developed a wide range of theories over the years to explain the role of these artifacts.

One of the most popular has been that the Romans used dodecahedra to study coins in some fashion. This theory would explain why dodecahedra's faces have so many holes. They'd place coins in them for study of some kind.

Two circumstantial pieces of evidence might support this theory. Firstly, many dodecahedra have been discovered as part of coin hoards in Britain, France, and elsewhere, suggesting that the Romans used them in association with coins in some fashion.

Secondly, the period to which the dodecahedra date between the late second century and the fourth century AD was one during

which successive Roman emperors began reducing the silver content of the leading Roman coins, the denarius, and the sesterce, as the empire ran into grave economic, political, and social problems.

Perhaps the dodecahedron emerged as a device that individuals used to try and gauge the silver content of individual coins? However, if this argument is valid, it is unclear how Romans used the device to accomplish this.

An Astronomical Device?

Others have proposed that these were astronomical devices that Romans used to study the stars by measuring distances between celestial bodies.

Knowing this might also have allowed the Romans to discover the best time for sowing crops and starting the harvest.

This theory might also explain why the dodecahedra were seemingly unique to the parts of the empire like Britain and Gaul, which Celtic tribes had formerly ruled.

These societies' druids and other religious figures placed great store in astrology. So it would make sense that the dodecahedra were most commonly used here if they were astronomical devices.

Decorative Objects, Candlesticks, or Children's Toys?

Many other theories have emerged over the years. For instance, archaeologists have found dodecahedra made from gold and other precious metals outside the Roman Empire in parts of Southeast Asia and India.

Consequently, some classical historians and archaeologists have speculated that the dodecahedra were effectively decorative ornaments, the use of which either arrived in the Roman Empire from the east or were transferred from Rome to the Far East.

Others still have speculated that the holes in the dodecahedra are indicative of the fact that they were used as candlestick holders. The discovery of the rarer icosahedra, many of which have symbols carved on their twenty faces, suggests that they were some children's toy or a kind of dice.

All of these theories have points to support them, but others are against them. For instance, if these were candlestick holders, why was their use seemingly confined to the north-western sections of the empire?

The Most Likely Answer: A Surveying Device?

While the preceding theories are hardly implausible and might well explain what a Roman dodecahedron was used for, the most likely answer for these twelve-sided objects is that they were used as a surveying device.

An individual could look through one of them and, if he knew how to use it, could measure how distant an object was and how long or wide it was.

For people who were some of the most skilled engineers in the pre-modern world and who were obsessed with building roads, aqueducts, temples, and military forts, an object of this kind would have been extremely useful.

It could have then been repurposed for astrological observations or even measuring the size of coins. Moreover, the frequency with which these objects appear in Britain, Gaul, Germania, and Noricum would be explained by the fact that these parts of the empire were the least developed when Rome first conquered them.

Greece, Egypt, and Syria, for instance, already had abundant temples, forts, and even primitive roads after being centers of advanced civilizations for centuries.

Conversely, Rome needed to develop new infrastructure across Northern Europe, which might explain why you would find surveying devices more frequently there.

However, even this is speculative. The reality is that, bar the unlikely chance of somebody uncovering a long-lost text which explains the dodecahedra, we may never know what these mysterious devices from Roman times were used for.

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What Was the Purpose of a Roman Dodecahedron?

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One of the significant advantages any historian of ancient Rome has is a wealth of written material that has survived from 2,000 years ago to help explain to us what the remains of the Roman Empire mean.