Octagonal-dodecagonal duoprismatic prism
Octagonal-dodecagonal duoprismatic prism | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Otwip |
Coxeter diagram | x x8o x12o |
Elements | |
Tera | 12 square-octagonal duoprisms, 8 square-dodecagonal duoprisms, 2 octagonal-dodecagonal duoprisms |
Cells | 96 cubes, 8+16 dodecagonal prisms, 12+24 octagonal prisms |
Faces | 96+96+192 squares, 24 octagons, 16 dodecagons |
Edges | 96+192+192 |
Vertices | 192 |
Vertex figure | Digonal disphenoidal pyramid, edge lengths √2+√2 (disphenoid base 1), √2+√3 (disphenoid base 2), √2 (remaining edges) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Sodip–op–sodip: 150° |
Sitwadip–twip–sitwadip: 135° | |
Sitwadip–cube–sodip: 90° | |
Otwadip–op–sodip: 90° | |
Sitwadip–twip–otwadip: 90° | |
Height | 1 |
Central density | 1 |
Number of external pieces | 22 |
Level of complexity | 30 |
Related polytopes | |
Army | Otwip |
Regiment | Otwip |
Dual | Octagonal-dodecagonal duotegmatic tegum |
Conjugates | Octagonal-dodecagrammic duoprismatic prism, Octagrammic-dodecagonal duoprismatic prism, Octagrammic-dodecagrammic duoprismatic prism |
Abstract & topological properties | |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | I2(8)×I2(12)×A1, order 768 |
Convex | Yes |
Nature | Tame |
The octagonal-dodecagonal duoprismatic prism or otwip, also known as the octagonal-dodecagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 octagonal-dodecagonal duoprisms, 8 square-dodecagonal duoprisms, and 12 square-octagonal duoprisms. Each vertex joins 2 square-octagonal duoprisms, 2 square-dodecagonal duoprisms, and 1 octagonal-dodecagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.
This polyteron can be alternated into a square-hexagonal duoantiprismatic antiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a hexagonal-square prismatic prismantiprismoid or the dodecagons into long ditrigons to create a square-hexagonal prismatic prismantiprismoid, which are also both nonuniform.
Vertex coordinates[edit | edit source]
The vertices of an octagonal-dodecagonal duoprismatic prism of edge length 1 are given by all permutations of the first two coordinates of:
Representations[edit | edit source]
An octagonal-dodecagonal duoprismatic prism has the following Coxeter diagrams:
- x x8o x12o (full symmetry)
- x x4x x12o (octagons as ditetragons)
- x x8o x6x (dodecagons as dihexagons)
- x x4x x6x
- xx8oo xx12oo&#x (octagonal-enneagonal duoprism atop octagonal-enneagonal duoprism)
- xx4xx xx12oo&#x
- xx8oo xx6xx&#x
- xx4xx xx6xx&#x