Mathematics · Study 062
Five Solids
The five Platonic solids as rotating wireframes: tetrahedron, cube, octahedron, dodecahedron and icosahedron, with their vertex, edge and face counts.
What you're looking at
Each solid is defined here only by its corner coordinates. The edges are found by measuring every pair of corners and keeping the pairs at the shortest distance. The face count is then deduced from Euler's formula, vertices minus edges plus faces equals two, and it comes out right every time.
The idea behind it
A Platonic solid has identical regular faces meeting the same way at every corner. Euclid ended the Elements with a proof that there are exactly five. The reason is simple: the angles meeting at a corner must total less than 360 degrees, and only five combinations of regular polygons manage it.
Try this
Click or tap for the next solid, or move the pointer to turn it. It changes every five seconds on its own.
