Pentagrammic-octagonal duoprism

Pentagrammic-octagonal duoprism
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Starodip
Coxeter diagram	x5/2o x8o()
Elements
Cells	8 pentagrammic prisms, 5 octagonal prisms
Faces	40 squares, 8 pentagrams, 5 octagons
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
Hypervolume
Dichoral angles	Stip–5/2–stip: 135°
	Stip–4–op: 90°
	Op–8–op: 36°
Central density	2
Number of external pieces	18
Level of complexity	12
Related polytopes
Army	Semi-uniform podip
Regiment	Starodip
Dual	Pentagrammic-octagonal duotegum
Conjugates	Pentagonal-octagonal duoprism, Pentagonal-octagrammic duoprism, Pentagrammic-octagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H2×I2(8), order 160
Convex	No
Nature	Tame

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

Vertex coordinates[edit | edit source]

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

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