Octagonal-decagonal duoprismatic prism
Octagonal-decagonal duoprismatic prism | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Oddip |
Coxeter diagram | x x8o x10o () |
Elements | |
Tera | 10 square-octagonal duoprisms, 8 square-decagonal duoprisms, 2 octagonal-decagonal duoprisms |
Cells | 80 cubes, 8+16 decagonal prisms, 10+20 octagonal prisms |
Faces | 80+80+160 squares, 20 octagons, 16 decagons |
Edges | 80+160+160 |
Vertices | 160 |
Vertex figure | Digonal disphenoidal pyramid, edge lengths √2+√2 (disphenoid base 1), √(5+√5)/2 (disphenoid base 2), √2 (remaining edges) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Sodip–op–sodip: 144° |
Squadedip–dip–squadedip: 135° | |
Squadedip–cube–sodip: 90° | |
Odedip–op–sodip: 90° | |
Squadedip–dip–odedip: 90° | |
Height | 1 |
Central density | 1 |
Number of external pieces | 20 |
Level of complexity | 30 |
Related polytopes | |
Army | Oddip |
Regiment | Oddip |
Dual | Octagonal-decagonal duotegmatic tegum |
Conjugates | Octagonal-decagrammic duoprismatic prism, Octagrammic-decagonal duoprismatic prism, Octagrammic-decagrammic duoprismatic prism |
Abstract & topological properties | |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | I2(8)×I2(10)×A1, order 640 |
Convex | Yes |
Nature | Tame |
The octagonal-decagonal duoprismatic prism or oddip, also known as the octagonal-decagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 octagonal-decagonal duoprisms, 8 square-decagonal duoprisms, and 10 square-octagonal duoprisms. Each vertex joins 2 square-octagonal duoprisms, 2 square-decagonal duoprisms, and 1 octagonal-decagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.
This polyteron can be alternated into a square-pentagonal duoantiprismatic antiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a pentagonal-square prismatic prismantiprismoid, which is also nonuniform.
Vertex coordinates[edit | edit source]
The vertices of an octagonal-decagonal duoprismatic prism of edge length 1 are given by all permutations of the first two coordinates of:
Representations[edit | edit source]
An octagonal-decagonal duoprismatic prism has the following Coxeter diagrams:
- x x8o x10o (full symmetry)
- x x4x x10o () (BC2×I2(10)×A1 symmetry, octagons as ditetragons)
- x x8o x5x () (H2×I2(8)×A1 symmetry, decagons as dipentagons)
- x x4x x5x () (BC2×H2×A1 symmetry)
- xx8oo xx10oo&#x (octagonal-decagonal duoprism atop octagonal-decagonal duoprism)
- xx4xx xx10oo&#x
- xx8oo xx5xx&#x
- xx4xx xx5xx&#x