600-cell |
Rectified 600-cell |
Rectified 120-cell |
120-cell |
| Orthogonal projections in H3 Coxeter plane | |||
|---|---|---|---|
In geometry, a rectified 600-cell is a uniform polychoron (4-dimensional uniform polytope) formed as the rectification of the regular 600-cell.
There are four rectifications of the 600-cell, including the zeroth, the 600-cell itself. Tbe birectified 600-cell is more easily seen as a rectified 120-cell, and the trirectified 600-cell is the same as the dual 120-cell.
|
| Rectified 600-cell | |
|---|---|
Schlegel diagram, shown as Birectified 120-cell, with 119 icosahedral cells colored |
|
| Type | Uniform polychoron |
| Uniform index | 34 |
| Schläfli symbol | t1{3,3,5} |
| Coxeter-Dynkin diagram | |
| Cells | 600 (3.3.3.3) 120 {3,5} |
| Faces | 1200+2400 {3} |
| Edges | 3600 |
| Vertices | 720 |
| Vertex figure | pentagonal prism |
| Symmetry group | H4 or [3,3,5] |
| Properties | convex, edge-transitive |
In geometry, the rectified 600-cell is a convex uniform polychoron composed of 600 regular octahedra and 120 icosahedra cells. Each edge has two octahedra and one icosahedron. Each vertex has five octahedra and two icosahedra. In total it has 3600 triangle faces, 3600 edges, and 720 vertices.
It is one of three semiregular polychora 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.
Containing the cell realms of both the regular 120-cell and the regular 600-cell, it can be considered analogous to the polyhedron icosidodecahedron, which is a rectified icosahedron and rectified dodecahedron.
The vertex figure of the rectified 600-cell is a uniform pentagonal prism.
| H4 | - | F4 |
|---|---|---|
[30] |
[20] |
[12] |
| H3 | A2 / B3 / D4 | A3 / B2 |
[10] |
[6] |
[4] |
| 120-cell | rectified 120-cell |
truncated 120-cell |
cantellated 120-cell |
runcinated 120-cell |
bitruncated 120-cell |
cantitruncated 120-cell |
runcitruncated 120-cell |
omnitruncated 120-cell |
|---|---|---|---|---|---|---|---|---|
| {5,3,3} | t1{5,3,3} | t0,1{5,3,3} | t0,2{5,3,3} | t0,3{5,3,3} | t1,2{5,3,3} | t0,1,2{5,3,3} | t0,1,3{5,3,3} | t0,1,2,3{5,3,3} |
| 600-cell | rectified 600-cell |
truncated 600-cell |
cantellated 600-cell |
runcinated 600-cell |
bitruncated 600-cell |
cantitruncated 600-cell |
runcitruncated 600-cell |
omnitruncated 600-cell |
| {3,3,5} | t1{3,3,5} | t0,1{3,3,5} | t0,2{3,3,5} | t0,3{3,3,5} | t1,2{3,3,5} | t0,1,2{3,3,5} | t0,1,3{3,3,5} | t0,1,2,3{3,3,5} |