A Platonic solid is a convex polyhedron whose faces are congruent regular polygons and whose vertex figures are all alike.
A regular icosahedron is a Platonic solid with twenty equilateral triangular faces, twelve vertices and thirty edges. Five faces meet at each vertex. Its orientation-preserving rotational symmetry has order sixty: the orbit-stabilizer theorem gives twenty faces times the three rotations stabilizing a chosen face.
A Platonic solid with six square faces, twelve edges and eight vertices. Its rotational symmetry group of a cube has order 24; including orientation-reversing isometries gives the order-48 symmetry group of a cube.
The regular dodecahedron is the Platonic solid with 12 regular pentagonal faces, 20 vertices, and 30 edges.
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A Platonic solid is a three-dimensional shape that is highly regular. Specifically, a Platonic solid comprises a set of identical polygonal faces, with the same number of faces meeting at each vertex. There are only five such solids, which are: 1. **Tetrahedron** - 4 triangular faces 2. **Cube (Hexahedron)** - 6 square faces 3. **Octahedron** - 8 triangular faces 4.
