Runcic 6-cube
(Redirected from Small rhombidemihexeract)
Runcic 6-cube | |
---|---|
Rank | 6 |
Type | Uniform |
Notation | |
Bowers style acronym | Sirhax |
Coxeter diagram | x3o3x3o3o *b3o () |
Elements | |
Peta | 32 birectified 5-simplices, 32 cantellated 5-simplices, 12 runcic 5-cubes |
Tera | 240 tetrahedral prisms, 192+192 rectified pentachora, 192 small rhombated pentachora, 60 rectified tesseracts |
Cells | 160+480+480 tetrahedra, 960 triangular prisms, 960 octahedra, 480 cuboctahedra |
Faces | 640+1920+1920 triangles, 1440 squares |
Edges | 960+2880 |
Vertices | 640 |
Vertex figure | Triangular-triangular pyramidal duoprism, edge lengths 1 (base triangular duoprism and top triangle), √2 (sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dipetal angles | Dot–rap–sarx: |
Sirhin–srip–sarx: | |
Sirhin–rap–dot: | |
Sarx–tepe–sarx: | |
Sirhin–rit–sirhin: 90° | |
Central density | 1 |
Number of external pieces | 76 |
Level of complexity | 40 |
Related polytopes | |
Army | Sirhax |
Regiment | Sirhax |
Conjugate | None |
Abstract & topological properties | |
Flag count | 921600 |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | D6, order 23040 |
Convex | Yes |
Nature | Tame |
The runcic 6-cube, also called the cantellated 6-demicube, small rhombidemihexeract, or sirhax, is a convex uniform 6-polytope. It consists of 12 runcic 5-cubes, 32 birectified 5-simplices, and 32 cantellated 5-simplices. 3 runcic 5-cubes, 1 birectified 5-simplex, and 3 cantellated 5-simplices join at each vertex. It can be consrtucted as a birectification of the 6-demicube.
Coordinates[edit | edit source]
The vertex coordinates of a runcic 6-cube, centered at the origin and with unit edge length, are given by all permutations and even sign changes of:
- .
Representations[edit | edit source]
A runcic 6-cube has the following Coxeter diagrams:
- x3o3x3o3o *b3o () (full symmetry)
- s4o3o3x3o3o () (as alternated runcinated 6-cube)
Gallery[edit | edit source]
-
B6 orthographic projection
-
D5
-
D4
-
D3
-
A5
-
A3
Related polytopes[edit | edit source]
The runcic 6-cube is the colonel of a regiment that includes 138 uniform members plus 15 fissaries.
External links[edit | edit source]
- Klitzing, Richard. "sirhax".
- Wikipedia contributors. "Runcic 6-cube".