Wisps

Shapes

There are five Platonic solids: tetrahedron, cube, octahedron, dodecahedron, icosahedron. They are the only ones in three dimensions that are regular, have congruent faces, and the same number of faces meeting at each vertex.

The tetrahedron is the simplest polyhedron. It has four faces, all triangles, six edges, and four vertices. It is is the shape of a four-sided die, an ammonia+ ion, and can be Sierpinskied into a fractal tetrahedron. Tetrahedra are probably beloved by some higher-dimension Vi Hart, as our three-dimesional one loves triangles.

Cubes (or "hexahedra") are probably the most familiar of the Platonic solids. It has six faces, twelve edges, and eight vertices. It is the shape of a familiar six-sided die, many containers, some building materials, pyrite crystals, and basically every block in Minecraft. The inverse of a cube is an octahedron.

Octohedra have, as evident in the name, eight faces. They also have twelve edges and six vertices. If you chop off the corners off until the edges of the cuts meet, you end up with a cube. Curiously enough, if you do the same thing to a cube, you end up with an octahedron. An octahedron is the shape of an eight-sided die and of fluorite crystals.

The Dodecahedron is a minor character in "The Phantom Tollbooth" by Norton Juster, who has a head in the shape of a dodecahedron with a different face on each face. There are twelve faces on a dodecahedron, along with 30 edges and 20 vertices. It is made entirely of pentagons. Dodecahedron-shaped things include 12-sided dice, those little bronze things found in Roman ruins, and the surface parts of the 120-cell polychoron.

Last, but not least, the icosahedron. It is made of triangles, like the octohedron and the tetrahedron, except it has 20 faces instead of 4 or 8, 30 edges, and 12 vertices. The only things I could find that are icosahedral in shape are 20-sided dice and some types of viruses. There are pyrite crystals that come close to being icosahedral, though.

HOORAY FOR PLATONIC SOLIDS !