Heptagonal-truncated octahedral duoprism
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Heptagonal-truncated octahedral duoprism | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Hetoe |
Coxeter diagram | x7o o4x3x () |
Elements | |
Tera | 6 square-heptagonal duoprisms, 8 hexagonal-heptagonal duoprisms, 7 truncated octahedral prisms |
Cells | 42 cubes, 56 hexagonal prisms, 12+24 heptagonal prisms, 7 truncated octahedra |
Faces | 42+84+168 squares, 56 hexagons, 42 heptagons |
Edges | 84+168+168 |
Vertices | 168 |
Vertex figure | Digonal disphenoidal pyramid, edge lengths √2, √3, √3 (base triangle), 2cos(π/7) (top), √2 (side edges) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Tope–toe–tope: |
Squahedip–hep–haheddip: | |
Haheddip–hep–haheddip: | |
Squahedip–cube–tope: 90° | |
Haheddip–hip–tope: 90° | |
Central density | 1 |
Number of external pieces | 21 |
Level of complexity | 30 |
Related polytopes | |
Army | Hetoe |
Regiment | Hetoe |
Dual | Heptagonal-tetrakis hexahedral duotegum |
Conjugates | Heptagrammic-truncated octahedral duoprism, Great heptagrammic-truncated octahedral duoprism |
Abstract & topological properties | |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | B3×I2(7), order 672 |
Convex | Yes |
Nature | Tame |
The heptagonal-truncated octahedral duoprism or hetoe is a convex uniform duoprism that consists of 7 truncated octahedral prisms, 8 hexagonal-heptagonal duoprisms, and 6 square-heptagonal duoprisms. Each vertex joins 2 truncated octahedral prisms, 1 square-heptagonal duoprism, and 2 hexagonal-heptagonal duoprisms.
Vertex coordinates[edit | edit source]
The vertices of a heptagonal-truncated octahedral duoprism of edge length 2sin(π/7) are given by all permutations of the last three coordinates of:
where j = 2, 4, 6.
Representations[edit | edit source]
A heptagonal-truncated octahedral duoprism has the following Coxeter diagrams:
- x7o o4x3x (full symmetry)
- x7o x3x3x ()
External links[edit | edit source]
- Klitzing, Richard. "n-toe-dip".