The Platonic Solids

• Tetrahedron
• Cube (hexahedron)
• Octahedron
• Icosahedron
• dodecahedron

Truncated, archimedean solids

• Truncated Cube
• Truncated Icosahedron

Stellated objects

• Great Dodecahedron
• Great Icosahedron
• Small Stellated Dodecahedron
• Great Stellated Dodecahedron

A number of 4-dimensional objects:

• The regular 8-cell consisting of 8 regular cubes
• The regular 600-cell consisting of 600 regular tetrahedra
• The regular 120-cell consisting of 120 regular dodecahedra

Here is why the regular 600- and 120-cell exist. Notice the tiny slit in the following

• Five tetrahedra around a common edge
• Three dodecahedra around a common edge