What is a Platonic solid?

Platonic solid, any of the five geometric solids with similar faces, regular polygons intersecting at the same three-dimensional angles. The Platonic solids, also known as regular solids or regular polyhedra, are convex polyhedra with identical faces made up of congruent convex regular polygons.

What is a Platonic solid 5e5?

5. A platonic solid is a 3D shape where each face is the same as a regular polygon and has the same number of faces meeting at each vertex. A regular, convex polyhedron with identical faces made up of congruent convex regular polygons is called a platonic solid.

When is a convex polyhedron a Platonic solid?

A convex polyhedron is a Platonic solid if and only if all its faces are congruent convex regular polygons, none of its faces intersect except at their edges, and the same number of faces meet at each of its vertices.

How are tessellations of the plane similar to the Platonic solids?

The three regular tessellations of the plane are closely related to the Platonic solids. Indeed, one can view the Platonic solids as regular tessellations of the sphere. This is done by projecting each solid onto a concentric sphere. The faces project onto regular spherical polygons which exactly cover the sphere.