Pentagonal-great enneagrammic duoprism

Pentagonal-great enneagrammic duoprism
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Pagstedip
Coxeter diagram	x5o x9/4o ()
Elements
Cells	9 pentagonal prisms, 5 great enneagrammic prisms
Faces	45 squares, 9 pentagons, 5 great enneagrams
Edges	45+45
Vertices	45
Vertex figure	Digonal disphenoid, edge lengths (1+√5)/2 (base 1), 2cos(4π/9) (base 2), √2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Gistep–9/4–gistep: 108°
	Pip–4–gistep: 90°
	Pip–5–pip: 20°
Central density	4
Number of external pieces	23
Level of complexity	12
Related polytopes
Army	Semi-uniform peendip
Regiment	Pagstedip
Dual	Pentagonal-great enneagrammic duotegum
Conjugates	Pentagonal-enneagonal duoprism, Pentagonal-enneagrammic duoprism, Pentagrammic-enneagonal duoprism, Pentagrammic-enneagrammic duoprism, Pentagrammic-great enneagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H2×I2(9), order 180
Convex	No
Nature	Tame

The pentagonal-great enneagrammic duoprism, also known as pagstedip or the 5-9/4 duoprism, is a uniform duoprism that consists of 9 pentagonal prisms and 5 great enneagrammic prisms, with two of each at each vertex.

Vertex coordinates[edit | edit source]

The vertex coordinates of a pentagonal-great enneagrammic duoprism, centered at the origin and with edge length 2sin(4π/9), are given by:

$\left(\pm \sin {\frac {4\pi }{9}},\,-{\sqrt {\frac {5+2{\sqrt {5}}}{5}}}\sin {\frac {4\pi }{9}},\,1,\,0\right),$
$\left(\pm \sin {\frac {4\pi }{9}},\,-{\sqrt {\frac {5+2{\sqrt {5}}}{5}}}\sin {\frac {4\pi }{9}},\,\cos \left({\frac {j\pi }{9}}\right),\,\pm \sin \left({\frac {j\pi }{9}}\right)\right),$
$\left(\pm \sin {\frac {4\pi }{9}},\,-{\sqrt {\frac {5+2{\sqrt {5}}}{5}}}\sin {\frac {4\pi }{9}},\,-{\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}}\right),$
$\left(\pm {\frac {1+{\sqrt {5}}}{2}}\sin {\frac {4\pi }{9}},\,{\sqrt {\frac {5-{\sqrt {5}}}{10}}}\sin {\frac {4\pi }{9}},\,1,\,0\right),$
$\left(\pm {\frac {1+{\sqrt {5}}}{2}}\sin {\frac {4\pi }{9}},\,{\sqrt {\frac {5-{\sqrt {5}}}{10}}}\sin {\frac {4\pi }{9}},\,\cos \left({\frac {j\pi }{9}}\right),\,\pm \sin \left({\frac {j\pi }{9}}\right)\right),$
$\left(\pm {\frac {1+{\sqrt {5}}}{2}}\sin {\frac {4\pi }{9}},\,{\sqrt {\frac {5-{\sqrt {5}}}{10}}}\sin {\frac {4\pi }{9}},\,-{\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}}\right),$
$\left(0,\,2{\sqrt {\frac {5+{\sqrt {5}}}{10}}}\sin {\frac {4\pi }{9}},\,1,\,0\right),$
$\left(0,\,2{\sqrt {\frac {5+{\sqrt {5}}}{10}}}\sin {\frac {4\pi }{9}},\,\cos \left({\frac {j\pi }{9}}\right),\,\pm \sin \left({\frac {j\pi }{9}}\right)\right),$
$\left(0,\,2{\sqrt {\frac {5+{\sqrt {5}}}{10}}}\sin {\frac {4\pi }{9}},\,-{\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}}\right),$