Rectified 7-simplex
(Redirected from Rectified octaexon)
Rectified 7-simplex | |
---|---|
Rank | 7 |
Type | Uniform |
Notation | |
Bowers style acronym | Roc |
Coxeter diagram | o3x3o3o3o3o3o () |
Elements | |
Exa | 8 heptapeta, 8 rectified heptapeta |
Peta | 56 hexatera, 28 rectified hexatera |
Tera | 168 pentachora, 56 rectified pentachora |
Cells | 280 tetrahedra, 70 octahedra |
Faces | 56+280 triangles |
Edges | 168 |
Vertices | 28 |
Vertex figure | Hexateric prism, edge length 1 |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diexal angles | Ril–hix–hop: |
Ril–rix–ril: | |
Height | |
Central density | 1 |
Number of external pieces | 16 |
Level of complexity | 6 |
Related polytopes | |
Army | Roc |
Regiment | Roc |
Conjugate | None |
Abstract & topological properties | |
Flag count | 241920 |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | A7, order 40320 |
Convex | Yes |
Nature | Tame |
The rectified octaexon, or roc, also called the rectified 7-simplex, is a convex uniform polyexon. It consists of 8 regular heptapeta and 8 rectified heptapeta. Two heptapeta and 6 rectified heptapeta join at each hexateric prismatic vertex. As the name suggests, it is the rectification of the octaexon.
It is also a convex segmentoexon, as heptapeton atop rectified heptapeton.
The hecatonicosihexapentacosiheptacontahexaexon, or 321 polytope, can be obtained as the convex hull of two oppositely oriented rectified octaexa.
Vertex coordinates[edit | edit source]
The vertices of a rectified octaexon of edge length 1 can be given in eight dimensions as all permutations of:
Representations[edit | edit source]
A rectified octaexon has the following Coxeter diagrams:
- o3x3o3o3o3o3o (full symmetry)
- xo3ox3oo3oo3oo3oo&#x (A6 axial, heptapeton atop rectified heptapeton)
- oxo oxo3oox3ooo3ooo3ooo&#xt (A5×A1 axial, vertex-first)
- xoo3oxo oxo3oox3ooo3ooo&#xt (A4×A2 axial, triangle-first)
- oxo3xoo3ooo oxo3oox3ooo&#xt (A3×A3 axial, octahedron-first)
External links[edit | edit source]
- Klitzing, Richard. "roc".
- Wikipedia contributors. "Rectified 7-simplex".