Omnitruncated 5-cube
(Redirected from Great cellated penteractitriacontaditeron)
Omnitruncated 5-cube | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Gacnet |
Coxeter diagram | x4x3x3x3x () |
Elements | |
Tera | 80 hexagonal-octagonal duoprisms, 80 truncated octahedral prisms, 40 great rhombicuboctahedral prisms, 32 great prismatodecachora, 10 great disprismatotesseractihexadecachora |
Cells | 480 cubes, 320+320+320+320 hexagonal prisms, 240+240 octagonal prisms, 160+160 truncated octahedra, 80 great rhombicuboctahedra |
Faces | 960+960+960+960+960+960 squares, 640+640+640 hexagons, 480 octagons |
Edges | 1920+1920+1920+1920+1920 |
Vertices | 3840 |
Vertex figure | Irregular pentachoron, edge lengths √2 (6), √3 (3), and √2+√2 (1) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Gippid–toe–tope: |
Tope–hip–hodip: 150° | |
Gircope–op–hodip: | |
Gippid–hip–hodip: | |
Gircope–cube–tope: 135° | |
Gidpith–girco–gircope: 135° | |
Gippid–hip–gircope: | |
Gidpith–op–hodip: | |
Gidpith–hip–tope: 120° | |
Gidpith–toe–gippid: | |
Central density | 1 |
Number of external pieces | 242 |
Level of complexity | 120 |
Related polytopes | |
Army | Gacnet |
Regiment | Gacnet |
Dual | Pentachoric trischilliaoctacositetracontateron |
Conjugate | Great quasicellipenteractitriacontaditeron |
Abstract & topological properties | |
Flag count | 460800 |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | B5, order 3840 |
Convex | Yes |
Nature | Tame |
The omnitruncated 5-cube, also called the great cellated penteractitriacontaditeron, great cellipenteractitriacontaditeron, or gacnet, is a convex uniform 5-polytope. It consists of 80 hexagonal-octagonal duoprisms, 80 truncated octahedral prisms, 40 great rhombicuboctahedral prisms, 32 great prismatodecachora, and 10 great disprismatotesseractihexadecachora. One of each type of facet joins at each vertex. As the name suggests, it is the omnitruncate of the B5 family.
This polyteron can be alternated into a snub penteract, although it cannot be made uniform.
Vertex coordinates[edit | edit source]
The vertices of an omnitruncated 5-cube of edge length 1 are given by all permutations of:
- .
Gallery[edit | edit source]
-
B4 or D5 orthographic projection
-
B3, D4, or A2
-
B2
-
A3
External links[edit | edit source]
- Bowers, Jonathan. "Category 10: greater truncates" (#743).
- Klitzing, Richard. "gacnet".
- Wikipedia contributors. "Omnitruncated 5-cube".