Decagonal-dodecahedral duoprism
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Decagonal-dodecahedral duoprism | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Dadoe |
Coxeter diagram | x10o x5o3o () |
Elements | |
Tera | 12 pentagonal-decagonal duoprisms, 10 dodecahedral prisms |
Cells | 120 pentagonal prisms, 30 decagonal prisms, 10 dodecahedra |
Faces | 300 squares, 120 pentagons, 20 decagons |
Edges | 200+300 |
Vertices | 200 |
Vertex figure | Triangular scalene, edge lengths (1+√5)/2 (base triangle), √(5+√5)/2 (top), √2 (sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Dope–doe–dope: 144° |
Padedip–dip–padedip: | |
Padedip–pip–dope: 90° | |
Central density | 1 |
Number of external pieces | 22 |
Level of complexity | 10 |
Related polytopes | |
Army | Dadoe |
Regiment | Dadoe |
Dual | Decagonal-icosahedral duotegum |
Conjugate | Decagrammic-great stellated dodecahedral duoprism |
Abstract & topological properties | |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | H3×I2(10), order 2400 |
Convex | Yes |
Nature | Tame |
The decagonal-dodecahedral duoprism or dadoe is a convex uniform duoprism that consists of 10 dodecahedral prisms and 12 pentagonal-decagonal duoprisms. Each vertex joins 2 dodecahedral prisms and 3 pentagonal-decagonal duoprisms.
Vertex coordinates[edit | edit source]
The vertices of a decagonal-dodecahedral duoprism of edge length 1 are given by:
as well as all even permutations of the last three coordinates of:
Representations[edit | edit source]
A decagonal-dodecahedral duoprism has the following Coxeter diagrams:
- x10o x5o3o ()(full symmetry)
- x5x x5o3o () (decagons as dipentagons)