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Maths of Planet Earth | Limitless Applications

A planet organized by humans

Published on May 15th, 2014 | by Liam

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# Neuroscientist discovers new solid shapes

To be regular, a three-dimensional solid needs all its faces to be the same regular shape. It also needs the same number of faces to meet at each corner. There are only five regular solids that meet all the rules. These five shapes are known as the Platonic solids. You already know some of these – the cube and the triangle-based pyramid. Others are less well known, including the octahedron and the 20-faced icosahedron.

So what happens if you only follow some of the regular solid rules? A scientist named Sam Schein found some regular-looking proteins while researching chemicals inside the eye. Sam looked for research into similar shapes, but almost every mathematical solid he found looked ugly. To work out why, Sam did some maths of his own. He discovered that the faces of these ugly solids weren’t flat!

Sam then set out to make his own solids. He wanted his solids to be symmetrical – you could rotate or reflect it and the solid would look the same. He also wanted all its faces to be flat, and all its edges to be equal lengths. To make it easier to find these solids, he allowed the angles on each face to be different. Some faces might have all angles equal, others might look squished or stretched, but the sides of each face would all be equal.

After an exhaustive search, Sam found an infinite number of solids that no-one had discovered before. Since they were based on real chemicals, they could be useful in medicine or chemistry. Or they might be useful in designing domes for high-tech buildings and greenhouses!

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