Hexagonal-great enneagrammic duoprism

Hexagonal-great enneagrammic duoprism
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Hagstedip
Coxeter diagram	x6o x9/4o ()
Elements
Cells	9 hexagonal prisms, 6 great enneagrammic prisms
Faces	54 squares, 9 hexagons, 6 great enneagrams
Edges	54+54
Vertices	54
Vertex figure	Digonal disphenoid, edge lengths √3 (base 1), 2cos(4π/9) (base 2), √2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Gistep–9/4–gistep: 120°
	Hip–4–gistep: 90°
	Hip–6–hip: 20°
Central density	4
Number of external pieces	24
Level of complexity	12
Related polytopes
Army	Semi-uniform hendip
Regiment	Hagstedip
Dual	Hexagonal-great enneagrammic duotegum
Conjugates	Hexagonal-enneagonal duoprism, Hexagonal-enneagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	G2×I2(9), order 216
Convex	No
Nature	Tame

The hexagonal-great enneagrammic duoprism, also known as hagstedip or the 6-9/4 duoprism, is a uniform duoprism that consists of 9 hexagonal prisms and 6 great enneagrammic prisms, with 2 of each at each vertex.

Vertex coordinates[edit | edit source]

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

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