Rectified 600-cell

It is one of three semiregular 4-polytopes made of two or more cells which are Platonic solids, discovered by Thorold Gosset in his 1900 paper. He called it a octicosahedric for being made of octahedron and icosahedron cells. E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as tC600. == Alternate names ==

• octicosahedric (Thorold Gosset) • Icosahedral hexacosihecatonicosachoron • Rectified 600-cell (Norman W. Johnson) • Rectified hexacosichoron • Rectified polytetrahedron • Rox (Jonathan Bowers) == Images ==

Diminished rectified 600-cell A related vertex-transitive polytope can be constructed with equal edge lengths removes 120 vertices from the rectified 600-cell, but isn't uniform because it contains square pyramid cells, discovered by George Olshevsky, calling it a swirlprismatodiminished rectified hexacosichoron, with 840 cells (600 square pyramids, 120 pentagonal prisms, and 120 pentagonal antiprisms), 2640 faces (1800 triangles, 600 square, and 240 pentagons), 2400 edges, and 600 vertices. It has a chiral bi-diminished pentagonal prism vertex figure. Each removed vertex creates a pentagonal prism cell, and diminishes two neighboring icosahedra into pentagonal antiprisms, and each octahedron into a square pyramid. This polytope can be partitioned into 12 rings of alternating 10 pentagonal prisms and 10 antiprisms, and 30 rings of square pyramids. Net H4 family Pentagonal prism vertex figures == References ==