Pentagrammic-hexagonal duoprism

Pentagrammic-hexagonal duoprism
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Stahdip
Coxeter diagram	x5/2o x6o ()
Elements
Cells	6 pentagrammic prisms, 5 hexagonal prisms
Faces	30 squares, 6 pentagrams, 5 hexagons
Edges	30+30
Vertices	30
Vertex figure	Digonal disphenoid, edge lengths (√5–1)/2 (base 1), √3 (base 2), √2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Stip–5/2–stip: 120°
	Stip–4–hip: 90°
	Hip–6–hip: 36°
Central density	2
Number of external pieces	16
Level of complexity	12
Related polytopes
Army	Semi-uniform phiddip
Regiment	Stahdip
Dual	Pentagrammic-hexagonal duotegum
Conjugate	Pentagonal-hexagonal duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H2×G2, order 120
Convex	No
Nature	Tame

The pentagrammic-hexagonal duoprism, also known as stahdip or the 5/2-6 duoprism, is a uniform duoprism that consists of 6 pentagrammic prisms and 5 hexagonal prisms, with 2 of each at each vertex.

Vertex coordinates[edit | edit source]

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

$\left(\pm {\frac {1}{2}},\,-{\sqrt {\frac {5-2{\sqrt {5}}}{20}}},\,\pm 1,\,0\right),$
$\left(\pm {\frac {1}{2}},\,-{\sqrt {\frac {5-2{\sqrt {5}}}{20}}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}}\right),$
$\left(\pm {\frac {{\sqrt {5}}-1}{4}},\,{\sqrt {\frac {5+{\sqrt {5}}}{40}}},\,\pm 1,\,0\right),$
$\left(\pm {\frac {{\sqrt {5}}-1}{4}},\,{\sqrt {\frac {5+{\sqrt {5}}}{40}}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}}\right),$
$\left(0,\,-{\sqrt {\frac {5-{\sqrt {5}}}{10}}},\,\pm 1,\,0\right),$
$\left(0,\,-{\sqrt {\frac {5-{\sqrt {5}}}{10}}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}}\right).$