Tetrachiliaenneacontahexahendon
Jump to navigation
Jump to search
Tetrachiliaenneacontahexahendon | |
---|---|
Rank | 12 |
Type | Regular |
Notation | |
Coxeter diagram | x3o3o3o3o3o3o3o3o3o3o4o () |
Schläfli symbol | {3,3,3,3,3,3,3,3,3,3,4} |
Elements | |
Henda | 4096 dodecadaka |
Daka | 24576 hendecaxenna |
Xenna | 67584 decayotta |
Yotta | 112640 enneazetta |
Zetta | 126720 octaexa |
Exa | 101376 heptapeta |
Peta | 59136 hexatera |
Tera | 25344 pentachora |
Cells | 7920 tetrahedra |
Faces | 1769 triangles |
Edges | 264 |
Vertices | 24 |
Vertex figure | Dischiliatetracontoctadakon, edge length 1 |
Measures (edge length 1) | |
Circumradius | |
Inradius | |
Hypervolume | |
Dihedral angle | |
Height | |
Central density | 1 |
Number of external pieces | 4096 |
Level of complexity | 1 |
Related polytopes | |
Army | * |
Regiment | * |
Dual | Dodekeract |
Conjugate | None |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | B12, order 1961990553600 |
Convex | Yes |
Nature | Tame |
The tetrachiliaenneacontahexahendon, also called the dodecacross or 12-orthoplex, is a regular polyhendon. It has 4096 regular dodecadaka as facets, joining 4 to a peak and 2048 to a vertex in a dischiliatetracontoctadakal arrangement. It is the 12-dimensional orthoplex. As such, it is a hexacontatetrapeton duotegum, hexadecachoron triotegum, octahedron tetrategum, and square hexategum.
Vertex coordinates[edit | edit source]
The vertices of a regular tetrachiliaenneacontahexahendon of edge length 1, centered at the origin, are given by all permutations of:
- .