Hendecagonal-hexagonal antiprismatic duoprism |
---|
|
Rank | 5 |
---|
Type | Uniform |
---|
Notation |
---|
Bowers style acronym | Henhap |
---|
Coxeter diagram | x11o s2s12o () |
---|
Elements |
---|
Tera | 11 hexagonal antiprismatic prisms, 12 triangular-hendecagonal duoprisms, 2 hexagonal-hendecagonal duoprisms |
---|
Cells | 132 triangular prisms, 22 hexagonal prisms, 11 hexagonal antiprisms, 12+12 hendecagonal prisms |
---|
Faces | 132 triangles, 132+132 squares, 22 hexagons, 12 hendecagons |
---|
Edges | 132+132+132 |
---|
Vertices | 132 |
---|
Vertex figure | Isosceles-trapezoidal scalene, edge lengths 1, 1, 1, √3 (base trapezoid), 2cos(π/11) (top), √2 (side edges) |
---|
Measures (edge length 1) |
---|
Circumradius | |
---|
Hypervolume | |
---|
Diteral angles | Happip–hap–happip: |
---|
| Thendip–henp–thendip: = |
---|
| Thendip–henp–hahendip: = |
---|
| Thendip–trip–happip: 90° |
---|
| Hahendip–hip–happip: 90° |
---|
Height | |
---|
Central density | 1 |
---|
Number of external pieces | 25 |
---|
Level of complexity | 40 |
---|
Related polytopes |
---|
Army | Henhap |
---|
Regiment | Henhap |
---|
Dual | Hendecagonal-hexagonal antitegmatic duotegum |
---|
Conjugates | Small hendecagrammic-hexagonal antiprismatic duoprism, Hendecagrammic-hexagonal antiprismatic duoprism, Great hendecagrammic-hexagonal antiprismatic duoprism, Grand hendecagrammic-hexagonal antiprismatic duoprism |
---|
Abstract & topological properties |
---|
Euler characteristic | 2 |
---|
Orientable | Yes |
---|
Properties |
---|
Symmetry | I2(11)×I2(12)×A1+, order 528 |
---|
Convex | Yes |
---|
Nature | Tame |
---|
The hendecagonal-hexagonal antiprismatic duoprism or henhap is a convex uniform duoprism that consists of 11 hexagonal antiprismatic prisms, 2 hexagonal-hendecagonal duoprisms, and 12 triangular-hendecagonal duoprisms. Each vertex joins 2 hexagonal antiprismatic prisms, 3 triangular-hendecagonal duoprisms, and 1 hexagonal-hendecagonal duoprism.
The vertices of a hendecagonal-hexagonal antiprismatic duoprism of edge length 2sin(π/11) are given by:
where j = 2, 4, 6, 8, 10.
A hendecagonal-hexagonal antiprismatic duoprism has the following Coxeter diagrams:
- x11o s2s12o (full symmetry; hexagonal antiprisms as alternated dodecagonal prisms)
- x11o s2s6s () (hexagonal antiprisms as alternated dihexagonal prisms)