Trirectified 8-cube
(Redirected from Trirectified octeract)
Trirectified 8-cube | |
---|---|
Rank | 8 |
Type | Uniform |
Notation | |
Bowers style acronym | Tro |
Coxeter diagram | o4o3o3x3o3o3o3o () |
Elements | |
Zetta | 256 birectified octaexa, 16 hepteractihecatonicosoctaexa |
Exa | 1024 rectified heptapeta, 2048 birectified heptapeta, 112 birectified hexacontatetrapeta |
Peta | 1792 hexatera, 7168 rectified hexatera, 7168 dodecatera, 448 rectified triacontaditera |
Tera | 10752 pentachora, 14336+21504 rectified pentachora, 1120 hexadecachora |
Cells | 17920+26880 tetrahedra, 35840 octahedra |
Faces | 35840+35840 triangles |
Edges | 26880 |
Vertices | 1792 |
Vertex figure | Octahedral-pentachoric duoprism, edge length 1 |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dizettal angles | Broc–ril–broc: |
Sez–bril–roc: | |
Sez–brag–sez: 90° | |
Central density | 1 |
Number of external pieces | 272 |
Level of complexity | 35 |
Related polytopes | |
Army | Tro |
Regiment | Tro |
Conjugate | None |
Abstract & topological properties | |
Flag count | 361267200 |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | B8, order 10321920 |
Convex | Yes |
Nature | Tame |
The trirectified octeract, or tro, also called the trirectified 8-cube, is a convex uniform polyzetton. It consists of 16 hepteractihecatonicosoctaexa and 256 birectified octaexa. 8 rectified octaexa and 5 hepteractihecatonicosoctaexa join at each octahedral-pentachoric duoprismatic vertex. As the name suggests, it is the trirectification of the octeract.
Vertex coordinates[edit | edit source]
The vertices of a trirectified octeract of edge length 1 are given by all permutations of:
Representations[edit | edit source]
A trirectified octeract has the following Coxeter diagrams:
- o4o3o3x3o3o3o3o (full symmetry)
- o3o3o *b3x3o3o3o3o (D8 symmetry)
- ooo4ooo3oxo3xox3ooo3ooo3ooo&#xt (B7 axial, hepteractihecatonicosoctaexon-first)
External links[edit | edit source]
- Klitzing, Richard. "tro".
- Wikipedia contributors. "Trirectified 8-cube".