Pentagrammic-octagrammic duoprism

Pentagrammic-octagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Stastodip
Coxeter diagram	x5/2o x8/3o ()
Elements
Cells	8 pentagrammic prisms, 5 octagrammic prisms
Faces	40 squares, 8 pentagrams, 5 octagrams
Edges	40+40
Vertices	40
Vertex figure	Digonal disphenoid, edge lengths (√5–1)/2 (base 1), √2–√2 (base 2), √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {15-5{\sqrt {2}}-{\sqrt {5}}}{10}}}\approx 0.75451$
Dichoral angles	Stip–4–stop: 90°
	Stip–5/2–stip: 45°
	Stop–8/3–stop: 36°
Central density	6
Number of external pieces	26
Level of complexity	24
Related polytopes
Army	Semi-uniform podip
Regiment	Stastodip
Dual	Pentagrammic-octagrammic duotegum
Conjugates	Pentagonal-octagonal duoprism, Pentagonal-octagrammic duoprism, Pentagrammic-octagonal duoprism
Abstract & topological properties
Flag count	960
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H2×I2(8), order 160
Convex	No
Nature	Tame

The pentagrammic-octagrammic duoprism, also known as stastodip or the 5/2-8/3 duoprism, is a uniform duoprism that consists of 8 pentagrammic prisms and 5 octagrammic prisms, with 2 of each at each vertex.

Vertex coordinates

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

• $\left(\pm {\frac {1}{2}},\,-{\sqrt {\frac {5-2{\sqrt {5}}}{20}}},\,\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {2}}-1}{2}}\right)$,
• $\left(\pm {\frac {1}{2}},\,-{\sqrt {\frac {5-2{\sqrt {5}}}{20}}},\,\pm {\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {1}{2}}\right)$,
• $\left(\pm {\frac {{\sqrt {5}}-1}{4}},\,{\sqrt {\frac {5+{\sqrt {5}}}{40}}},\,\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {2}}-1}{2}}\right)$,
• $\left(\pm {\frac {{\sqrt {5}}-1}{4}},\,{\sqrt {\frac {5+{\sqrt {5}}}{40}}},\,\pm {\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {1}{2}}\right)$,
• $\left(0,\,-{\sqrt {\frac {5-{\sqrt {5}}}{10}}},\,\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {2}}-1}{2}}\right)$,
• $\left(0,\,-{\sqrt {\frac {5-{\sqrt {5}}}{10}}},\,\pm {\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {1}{2}}\right)$.

Representations

A pentagrammic-octagrammic duoprism has the following Coxeter diagrams:

• x5/2o x8/3o () (full symmetry)
• x4/3x x5/2o () (B₂×H₂ symmetry, octagrams as ditetragrams)

External links

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

• Klitzing, Richard. "stastodip".