There are, up to similarity, exactly five Platonic solids:

• the tetrahedron, with 4 triangular faces and 4 vertices,
• the cube, with 6 square faces and 8 vertices,
• the octahedron, with 8 triangular faces and 6 vertices,
• the dodecahedron, with 12 pentagonal faces and 20 vertices,
• the icosahedron, with 20 triangular faces and 12 vertices.