Heptagrammic-great enneagrammic duoprism

Heptagrammic-great enneagrammic duoprism
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Shegstedip
Coxeter diagram	x7/2o x9/4o ()
Elements
Cells	9 heptagrammic prisms, 7 great enneagrammic prisms
Faces	63 squares, 9 heptagrams, 7 great enneagrams
Edges	63+63
Vertices	63
Vertex figure	Digonal disphenoid, edge lengths 2cos(2π/7) (base 1), 2cos(4π/9) (base 2), √2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Ship–4–gistep: 90°
	Gistep–9/4–gistep:
	Ship–7/2–ship: 20°
Central density	8
Number of external pieces	32
Level of complexity	24
Related polytopes
Army	Semi-uniform heendip
Regiment	Shegstedip
Dual	Heptagrammic-great enneagrammic duotegum
Conjugates	Heptagonal-enneagonal duoprism, Heptagonal-enneagrammic duoprism, Heptagonal-great enneagrammic duoprism, Heptagrammic-enneagonal duoprism, Heptagrammic-enneagrammic duoprism, Great heptagrammic-enneagonal duoprism, Great heptagrammic-enneagrammic duoprism, Great heptagrammic-great enneagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(7)×I2(9), order 252
Convex	No
Nature	Tame

The heptagrammic-great enneagrammic duoprism or shegstedip, also known as the 7/2-9/4 duoprism, is a uniform duoprism that consists of 9 heptagrammic prisms and 7 great enneagrammic prisms, with 2 of each at each vertex.

Vertex coordinates[edit | edit source]

The coordinates of a heptagrammic-great enneagrammic duoprism, centered at the origin and with edge length 4sin(2π/7)sin(4π/9), are given by:

$\left(2\sin {\frac {4\pi }{9}},\,0,\,2\sin {\frac {2\pi }{7}},\,0\right),$
$\left(2\sin {\frac {4\pi }{9}},\,0,\,2\sin {\frac {2\pi }{7}}\cos \left({\frac {k\pi }{9}}\right),\,\pm 2\sin {\frac {2\pi }{7}}\sin \left({\frac {k\pi }{9}}\right)\right),$
$\left(2\sin {\frac {4\pi }{9}},\,0,\,-\sin {\frac {2\pi }{7}},\,\pm {\sqrt {3}}\sin {\frac {2\pi }{7}}\right),$
$\left(2\sin {\frac {4\pi }{9}}\cos \left({\frac {j\pi }{7}}\right),\,\pm 2\sin {\frac {4\pi }{9}}\sin \left({\frac {j\pi }{7}}\right),\,2\sin {\frac {2\pi }{7}},\,0\right),$
$\left(2\sin {\frac {4\pi }{9}}\cos \left({\frac {j\pi }{7}}\right),\,\pm 2\sin {\frac {4\pi }{9}}\sin \left({\frac {j\pi }{7}}\right),\,2\sin {\frac {2\pi }{7}}\cos \left({\frac {k\pi }{9}}\right),\,\pm 2\sin {\frac {2\pi }{7}}\sin \left({\frac {k\pi }{9}}\right)\right),$
$\left(2\sin {\frac {4\pi }{9}}\cos \left({\frac {j\pi }{7}}\right),\,\pm 2\sin {\frac {4\pi }{9}}\sin \left({\frac {j\pi }{7}}\right),\,-\sin {\frac {2\pi }{7}},\,\pm {\sqrt {3}}\sin {\frac {2\pi }{7}}\right),$