Rectified 8-orthoplex
(Redirected from Rectified diacosipentacontahexazetton)
Rectified 8-orthoplex | |
---|---|
Rank | 8 |
Type | Uniform |
Notation | |
Bowers style acronym | Rek |
Coxeter diagram | o4o3o3o3o3o3x3o () |
Elements | |
Zetta | 256 rectified octaexa, 16 hecatonicosoctaexa |
Exa | 2048 heptapeta, 1024 rectified heptapeta |
Peta | 7168 hexatera, 1792 rectified hexatera |
Tera | 10752 pentachora, 1792 rectified pentachora |
Cells | 8960 tetrahedra, 1120 octahedra |
Faces | 448+4480 triangles |
Edges | 1344 |
Vertices | 112 |
Vertex figure | Hexacontatetrapetic prism, edge length 1 |
Measures (edge length 1) | |
Circumradius | 1 |
Hypervolume | |
Dizettal angles | Roc–ril–roc: |
Zee–hop–roc: | |
Central density | 1 |
Number of external pieces | 272 |
Level of complexity | 7 |
Related polytopes | |
Army | Rek |
Regiment | Rek |
Conjugate | None |
Abstract & topological properties | |
Flag count | 72253440 |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | B8, order 10321920 |
Convex | Yes |
Nature | Tame |
The rectified diacosipentacontahexazetton, or rek, also called the rectified 8-orthoplex, is a convex uniform polyzetton. It consists of 16 regular hecatonicosoctaexa and 256 rectified octaexa. Two hecatonicosoctaexa and 64 rectified octaexa join at each hexacontatetrapetic prismatic vertex. As the name suggests, it is the rectification of the diacosipentacontahexazetton.
The rectified diacosipentacontahexazetton can be vertex-inscribed into the dischiliahecatonhexaconta-myriaheptachiliadiacosioctaconta-zetton (or 421 polytope).
Vertex coordinates[edit | edit source]
The vertices of a rectified diacosipentacontahexazetton of edge length 1 are given by all permutations of:
Representations[edit | edit source]
A rectified diacosipentacontahexazetton has the following Coxeter diagrams:
- o4o3o3o3o3o3x3o (full symmetry)
- o3o3o *b3o3o3o3x3o (D8 symmetry)
- ooo4ooo3ooo3ooo3ooo3oxo3xox&#xt (B7 axial, hecatonicosoctaexon-first)
External links[edit | edit source]
- Klitzing, Richard. "rek".
- Wikipedia contributors. "Rectified 8-orthoplex".