Octagonal-decagrammic duoprism

Octagonal-decagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Ostadedip
Coxeter diagram	x8o x10/3o ()
Elements
Cells	10 octagonal prisms, 8 decagrammic prisms
Faces	80 squares, 10 octagons, 8 decagrams
Edges	80+80
Vertices	80
Vertex figure	Digonal disphenoid, edge lengths √2+√2 (base 1), √(5–√5)/2 (base 2), √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {5+{\sqrt {2}}-{\sqrt {5}}}{2}}}\approx 1.44536$
Hypervolume	$5{\sqrt {15+10{\sqrt {2}}+-6{\sqrt {5}}-4{\sqrt {10}}}}\approx 8.77014$
Dichoral angles	Stiddip–10/3–stiddip: 135°
	Op–4–stiddip: 90°
	Op–8–op: 72°
Central density	3
Number of external pieces	28
Level of complexity	12
Related polytopes
Army	Semi-uniform odedip
Regiment	Ostadedip
Dual	Octagonal-decagrammic duotegum
Conjugates	Octagonal-decagonal duoprism, Octagrammic-decagonal duoprism, Octagrammic-decagrammic duoprism
Abstract & topological properties
Flag count	1920
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(8)×I2(10), order 320
Convex	No
Nature	Tame

The octagonal-decagrammic duoprism, also known as ostadedip or the 8-10/3 duoprism, is a uniform duoprism that consists of 10 octagonal prisms and 8 decagrammic prisms, with 2 of each at each vertex.

Vertex coordinates

The coordinates of a octagonal-decagrammic duoprism, centered at the origin and with unit edge length, are given by:

• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {5-2{\sqrt {5}}}}{2}}\right)$,
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\sqrt {\frac {5-{\sqrt {5}}}{8}}}\right)$,
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,0\right)$,
• $\left(\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {5-2{\sqrt {5}}}}{2}}\right)$,
• $\left(\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\sqrt {\frac {5-{\sqrt {5}}}{8}}}\right)$,
• $\left(\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,0\right)$.

Representations

An octagonal-decagrammic duoprism has the following Coxeter diagrams:

• x8o x10/3o () (full symmetry)
• x4x x10/3o () (B₂×I₂(10) symmetry, octagons as ditetragons)
• x5/3x x8o () (H₂×I₂(8) symmetry, decagons as dipentagons)
• x4x x5/3x () (B₂×H₂ symmetry)

External links

• Bowers, Jonathan. "Category A: Duoprisms".

• Klitzing, Richard. "nd-mb-dip".