Enneagrammic-great enneagrammic duoprism

Enneagrammic-great enneagrammic duoprism
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Stegstedip
Coxeter diagram	x9/2o x9/4o ()
Elements
Cells	9 enneagrammic prisms, 9 great enneagrammic prisms
Faces	81 squares, 9 enneagrams, 9 great enneagrams
Edges	81+81
Vertices	81
Vertex figure	Digonal disphenoid, edge lengths 2cos(2π/9) (base 1), 2cos(4π/9) (base 2), √2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Gistep–9/4–gistep: 100°
	Step–4–gistep: 90°
	Step–9/2–step: 20°
Central density	8
Number of external pieces	36
Level of complexity	24
Related polytopes
Army	Semi-uniform edip
Regiment	Stegstedip
Dual	Enneagrammic-great enneagrammic duotegum
Conjugates	Enneagonal-enneagrammic duoprism, Enneagonal-great enneagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(9)×I2(9), order 324
Convex	No
Nature	Tame

The enneagrammic-great enneagrammic duoprism or stegstedip, also known as the 9/2-9/4 duoprism, is a uniform duoprism that consists of 9 enneagrammic prisms and 9 great enneagrammic prisms, with 2 of each at each vertex.

Coordinates[edit | edit source]

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

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