The pentachoron, hypercube, orthoplex, hecatonicosachoron, and hexacosichoron are analogues of the ordinary Platonic solids. |
A 3-simplex is usually called a tetrahedron, and the 4-simplex, which is the basic building block in this theory, is also known as the pentatope, or pentachoron. |
Geometrically, K3 relates to a triangle, K4 a tetrahedron, K5 a pentachoron, etc. |