Decagonal-hendecagonal duoprismatic prism |
---|
|
Rank | 5 |
---|
Type | Uniform |
---|
Notation |
---|
Bowers style acronym | Dahenip |
---|
Coxeter diagram | x x10o x11o () |
---|
Elements |
---|
Tera | 11 square-decagonal duoprisms, 10 square-hendecagonal duoprisms, 2 decagonal-hendecagonal duoprisms |
---|
Cells | 110 cubes, 10+20 hendecagonal prisms, 11+22 decagonal prisms |
---|
Faces | 110+110+220 squares, 22 decagons, 20 hendecagons |
---|
Edges | 110+220+220 |
---|
Vertices | 220 |
---|
Vertex figure | Digonal disphenoidal pyramid, edge lengths √(5+√5)/2 (disphenoid base 1), 2cos(π/11) (disphenoid base 2), √2 (remaining edges) |
---|
Measures (edge length 1) |
---|
Circumradius | |
---|
Hypervolume | |
---|
Diteral angles | Squadedip–dip–squadedip: |
---|
| Shendip–henp–shendip: 144° |
---|
| Shendip–cube–squadedip: 90° |
---|
| Dahendip–dip–squadedip: 90° |
---|
| Shendip–henp–dahendip: 90° |
---|
Height | 1 |
---|
Central density | 1 |
---|
Number of external pieces | 23 |
---|
Level of complexity | 30 |
---|
Related polytopes |
---|
Army | Dahenip |
---|
Regiment | Dahenip |
---|
Dual | Decagonal-hendecagonal duotegmatic tegum |
---|
Conjugates | Decagonal-small hendecagrammic duoprismatic prism, Decagonal-hendecagrammic duoprismatic prism, Decagonal-great hendecagrammic duoprismatic prism, Decagonal-grand hendecagrammic duoprismatic prism, Decagrammic-hendecagonal duoprismatic prism, Decagrammic-small hendecagrammic duoprismatic prism, Decagrammic-hendecagrammic duoprismatic prism, Decagrammic-great hendecagrammic duoprismatic prism, Decagrammic-grand hendecagrammic duoprismatic prism |
---|
Abstract & topological properties |
---|
Euler characteristic | 2 |
---|
Orientable | Yes |
---|
Properties |
---|
Symmetry | I2(10)×I2(11)×A1, order 880 |
---|
Convex | Yes |
---|
Nature | Tame |
---|
The decagonal-hendecagonal duoprismatic prism or dahenip, also known as the decagonal-hendecagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 decagonal-hendecagonal duoprisms, 10 square-hendecagonal duoprisms, and 11 square-decagonal duoprisms. Each vertex joins 2 square-decagonal duoprisms, 2 square-hendecagonal duoprisms, and 1 decagonal-hendecagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.
The vertices of an decagonal-hendecagonal duoprismatic prism of edge length 2sin(π/11) are given by:
where j = 2, 4, 6, 8, 10.
A decagonal-hendecagonal duoprismatic prism has the following Coxeter diagrams:
- x x10o x11o () (full symmetry)
- x x5x x11o () (decagons as dipentagons)
- xx10oo xx11oo&#x (decagonal-hendecagonal duoprism atop decagonal-hendecagonal duoprism)
- xx5xx xx11oo&#x