Decagrammic duoprism
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Decagrammic duoprism | |
---|---|
Rank | 4 |
Type | Uniform |
Notation | |
Bowers style acronym | Stadidip |
Coxeter diagram | x10/3o x10/3o () |
Elements | |
Cells | 20 decagrammic prisms |
Faces | 100 squares, 20 decagrams |
Edges | 200 |
Vertices | 100 |
Vertex figure | Tetragonal disphenoid, edge lengths √(5–√5)/2 (bases) and √2 (sides) |
Measures (edge length 1) | |
Circumradius | |
Inradius | |
Hypervolume | |
Dichoral angles | Stiddip–4–stiddip: 90° |
Stiddip–10/3–stiddip: 72° | |
Central density | 9 |
Number of external pieces | 40 |
Level of complexity | 12 |
Related polytopes | |
Army | Dedip |
Regiment | Stadidip |
Dual | Decagrammic duotegum |
Conjugate | Decagonal duoprism |
Abstract & topological properties | |
Flag count | 2400 |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | I2(10)≀S2, order 800 |
Convex | No |
Nature | Tame |
The decagrammic duoprism or stadidip, also known as the decagrammic-decagrammic duoprism, the 10/3 duoprism or the 10/3-10/3 duoprism, is a noble uniform duoprism that consists of 20 decagrammic prisms, with 4 meeting at each vertex.
A unit decagrammic duoprism can be vertex-inscribed into a grand ditetrahedronary hexacosidishecatonicosachoron.
Vertex coordinates[edit | edit source]
The coordinates of a decagrammic duoprism, centered at the origin and with unit edge length, are given by:
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- ,
- .
Representations[edit | edit source]
A decagrammic duoprism duoprism has the following Coxeter diagrams:
- x10/3o x10/3o () (full symmetry)
- x5/3x x10/3o () (H2×I2(10) symmetry, some decagons as dipentagons)
- x5/3x x5/3x () (H2≀S2 symmetry, all decagons as dipentagons)
External links[edit | edit source]
- Bowers, Jonathan. "Category A: Duoprisms".
- Klitzing, Richard. "stadidip".