Dodecagonal-truncated octahedral duoprism
Dodecagonal-truncated octahedral duoprism | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Twatoe |
Coxeter diagram | x12o o4x3x () |
Elements | |
Tera | 6 square-dodecagonal duoprisms, 12 truncated octahedral prisms, 8 hexagonal-dodecagonal duoprisms |
Cells | 72 cubes, 96 hexagonal prisms, 12+24 dodecagonal prisms, 12 truncated octahedra |
Faces | 72+144+288 squares, 96 hexagons, 24 dodecagons |
Edges | 144+288+288 |
Vertices | 288 |
Vertex figure | Digonal disphenoidal pyramid, edge lengths √2, √3, √3 (base triangle), √2+√3 (top), √2 (side edges) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Tope–toe–tope: 150° |
Sitwadip–twip–hitwadip: | |
Hitwadip–twip–hitwadip: | |
Sitwadip–cube–tope: 90° | |
Hitwadip–hip–tope: 90° | |
Central density | 1 |
Number of external pieces | 26 |
Level of complexity | 30 |
Related polytopes | |
Army | Twatoe |
Regiment | Twatoe |
Dual | Dodecagonal-tetrakis hexahedral duotegum |
Conjugate | Dodecagrammic-truncated octahedral duoprism |
Abstract & topological properties | |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | B3×I2(12), order 1152 |
Convex | Yes |
Nature | Tame |
The dodecagonal-truncated octahedral duoprism or twatoe is a convex uniform duoprism that consists of 12 truncated octahedral prisms, 8 hexagonal-dodecagonal duoprisms, and 6 square-dodecagonal duoprisms. Each vertex joins 2 truncated octahedral prisms, 1 square-dodecagonal duoprism, and 2 hexagonal-dodecagonal duoprisms.
This polyteron can be alternated into a hexagonal-pyritohedral icosahedral duoantiprism, although it cannot be made uniform. The dodecagons can also be alternated into long ditrigons to create a pyritohedral icosahedral-hexagonal prismantiprismoid, which is also nonuniform.
Vertex coordinates[edit | edit source]
The vertices of a dodecagonal-truncated octahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of:
Representations[edit | edit source]
A dodecagonal-truncated octahedral duoprism has the following Coxeter diagrams:
- x12o o4x3x () (full symmetry)
- x12o x3x3x ()
- x6x o4x3x () (dodecagons as dihexagons)
- x6x x3x3x ()