Enneagrammic duoprism

Enneagrammic duoprism
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Stedip
Coxeter diagram	x9/2o x9/2o ()
Elements
Cells	18 enneagrammic prisms
Faces	81 squares, 18 enneagrams
Edges	162
Vertices	81
Vertex figure	Tetragonal disphenoid, edge lengths 2cos(2π/9) (bases) and √2 (sides)
Measures (edge length 1)
Circumradius
Inradius
Hypervolume
Dichoral angles	Step–9/2–step: 100°
	Step–4–step: 90°
Central density	4
Number of external pieces	36
Level of complexity	12
Related polytopes
Army	Edip
Regiment	Stedip
Dual	Enneagrammic duotegum
Conjugates	Enneagonal duoprism, Great enneagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(9)≀S2, order 648
Convex	No
Nature	Tame

The enneagrammic duoprism or stedip, also known as the enneagrammic-enneagrammic duoprism, the 9/2 duoprism or the 9/2-9/2 duoprism, is a noble uniform duoprism that consists of 18 enneagrammic prisms, with 4 meeting at each vertex.

The name can also refer to the great enneagrammic duoprism or the enneagrammic-great enneagrammic duoprism.

Vertex coordinates[edit | edit source]

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

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