Pentagrammic-great hendecagrammic duoprism

Pentagrammic-great hendecagrammic duoprism
	(OFF file)
Rank	4
Type	Uniform
Notation
Coxeter diagram	x5/2o x11/4o ()
Elements
Cells	11 pentagrammic prisms, 5 great hendecagrammic prisms
Faces	55 squares, 11 pentagrams, 5 great hendecagrams
Edges	55+55
Vertices	55
Vertex figure	Digonal disphenoid, edge lengths (√5–1)/2 (base 1), 2cos(4π/11) (base 2), √2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Stip–4–gishenp: 90°
	Stip–5/2–stip:
	Gishenp–11/4–gishenp: 36°
Central density	8
Number of external pieces	32
Level of complexity	24
Related polytopes
Army	Semi-uniform pahendip
Dual	Pentagrammic-great hendecagrammic duotegum
Conjugates	Pentagonal-hendecagonal duoprism, Pentagonal-small hendecagrammic duoprism, Pentagonal-hendecagrammic duoprism, Pentagonal-great hendecagrammic duoprism, Pentagonal-grand hendecagrammic duoprism, Pentagrammic-hendecagonal duoprism, Pentagrammic-small hendecagrammic duoprism, Pentagrammic-hendecagrammic duoprism, Pentagrammic-grand hendecagrammic duoprism
Abstract & topological properties
Flag count	1320
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H2×I2(11), order 220
Convex	No
Nature	Tame

The pentagrammic-great hendecagrammic duoprism, also known as the 5/2-11/4 duoprism, is a uniform duoprism that consists of 11 pentagrammic prisms and 5 great hendecagrammic prisms, with 2 of each at each vertex.

Vertex coordinates[edit | edit source]

The coordinates of a pentagrammic-great hendecagrammic duoprism, centered at the origin and with edge length 2sin(4π/11), are given by:

$\left(\pm \sin {\frac {4\pi }{11}},\,-{\sqrt {\frac {5-2{\sqrt {5}}}{5}}}\sin {\frac {4\pi }{11}},\,1,\,0\right)$ ,
$\left(\pm \sin {\frac {4\pi }{11}},\,-{\sqrt {\frac {5-2{\sqrt {5}}}{5}}}\sin {\frac {4\pi }{11}},\,\cos \left({\frac {j\pi }{11}}\right),\,\pm \sin \left({\frac {j\pi }{11}}\right)\right)$ ,
$\left(\pm {\frac {{\sqrt {5}}-1}{2}}\sin {\frac {4\pi }{11}},\,{\sqrt {\frac {5+{\sqrt {5}}}{10}}}\sin {\frac {4\pi }{11}},\,1,\,0\right)$ ,
$\left(\pm {\frac {{\sqrt {5}}-1}{2}}\sin {\frac {4\pi }{11}},\,{\sqrt {\frac {5+{\sqrt {5}}}{10}}}\sin {\frac {4\pi }{11}},\,\cos \left({\frac {j\pi }{11}}\right),\,\pm \sin \left({\frac {j\pi }{11}}\right)\right)$ ,
$\left(0,\,-2{\sqrt {\frac {5-{\sqrt {5}}}{10}}}\sin {\frac {4\pi }{11}},\,1,\,0\right)$ ,
$\left(0,\,-2{\sqrt {\frac {5-{\sqrt {5}}}{10}}}\sin {\frac {4\pi }{11}},\,\cos \left({\frac {j\pi }{11}}\right),\,\pm \sin \left({\frac {j\pi }{11}}\right)\right)$ ,