Pentitruncated 6-cube
Pentitruncated 6-cube | |
---|---|
Rank | 6 |
Type | Uniform |
Notation | |
Bowers style acronym | Tacog |
Coxeter diagram | x4x3o3o3o3x () |
Elements | |
Peta | 192 pentachoric prisms 64 stericated 5-simplices 240 octagonal-tetrahedral duoprisms 60 truncated tesseractic prisms 160 triangular-truncated cubic duoprisms 12 truncated 5-cubes |
Tera | 384+384 pentachora 960+960+960 tetrahedral prisms 1280 triangular duoprisms 960 triangular-octagonal duoprisms 480 truncated cubic prisms 120 truncated tesseracts |
Cells | 1920+1920 tetrahedra 1920+3840+3840 triangular prisms 1440 octagonal prisms 480 truncated cubes |
Faces | 3840+3840 triangles, 1920+5760 squares, 960 octagons |
Edges | 960+3840+3840 |
Vertices | 1920 |
Vertex figure | Skew tetrahedral antiprismatic pyramid, edge lengths 1 (base tetrahedra), √2 (sides of antiprism and lacings to one base), and √2+√2 (lacings to other base) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dipetal angles | Scad–pen–penp: |
Penp–tepe–otet: | |
Otet–todip–tratic: 150° | |
Scad–tepe–otet: | |
Tattip–ticcup–tratic: | |
Scad–triddip–tratic 135° | |
Tan–tat–tattip: 135° | |
Scad–tepe–tattip: | |
Central density | 1 |
Number of external pieces | 728 |
Level of complexity | 96 |
Related polytopes | |
Army | Tacog |
Regiment | Tacog |
Conjugate | Quasitericellated hexacontatetrapeton |
Abstract & topological properties | |
Flag count | 4423680 |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | B6, order 46080 |
Convex | Yes |
Nature | Tame |
The pentitruncated 6-cube, also called the pentitruncated dodecapeton, tericellated hexacontatetrapeton, or tacog, is a convex uniform 6-polytope. It consists of 12 truncated 5-cubes, 64 stericated 5-simplices, 192 pentachoric prisms, 60 truncated tesseractic prisms, 240 octagonal-tetrahedral duoprisms, and 160 triangular-truncated cubic duoprisms. 1 truncated 5-cube, 1 stericated 5-simplex, 1 pentachoric prism, 4 truncated tesseractic prisms, 4 octagonal-tetrahedral duoprisms, and 6 triangular-truncated cubic duoprisms join at each vertex. As the name suggests, it is the pentitruncation of the 6-cube.
Vertex coordinates[edit | edit source]
The coordinates of a pentitruncated 6-cube, centered at the origin and with unit edge length, are given by all permutations of:
- .
Gallery[edit | edit source]
-
B5 orthographic projection
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B4
-
B3
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B2
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A5
-
A3
Related polytopes[edit | edit source]
The regiment of the pentitruncated 6-cube contains 15 uniform members.
External links[edit | edit source]
- Klitzing, Richard. "tacog".
- Wikipedia contributors. "Pentitruncated 6-cube".