Heptagonal-heptagrammic duoprism

Heptagonal-heptagrammic duoprism
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Heshedip
Coxeter diagram	x7o x7/2o ()
Elements
Cells	7 heptagonal prisms, 7 heptagrammic prisms
Faces	49 squares, 7 heptagons, 7 heptagrams
Edges	49+49
Vertices	49
Vertex figure	Digonal disphenoid, edge lengths 2cos(π/7) (base 1), 2cos(2π/7) (base 2), √2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Ship–7/2–ship:
	Hep–4–ship:
	Hep–7–hep:
Central density	2
Number of external pieces	21
Level of complexity	12
Related polytopes
Army	Semi-uniform hedip
Regiment	Heshedip
Dual	Heptagonal-heptagrammic duotegum
Conjugates	Heptagonal-great heptagrammic duoprism, Heptagrammic-great heptagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(7)×I2(7), order 196
Convex	No
Nature	Tame

The heptagonal-heptagrammic duoprism, also known as heshedip or the 7-7/2 duoprism, is a uniform duoprism that consists of 7 heptagonal prisms and 7 heptagrammic prisms, with 2 of each at each vertex.

The name can also refer to the heptagonal-great heptagrammic duoprism.

Vertex coordinates[edit | edit source]

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

$\left(2\cos {\frac {\pi }{7}},\,0,\,1,\,0\right),$
$\left(2\cos {\frac {\pi }{7}},\,0,\,\cos \left({\frac {k\pi }{7}}\right),\,\pm \sin \left({\frac {k\pi }{7}}\right)\right),$
$\left(2\cos {\frac {\pi }{7}}\cos \left({\frac {j\pi }{7}}\right),\,\pm 2\cos {\frac {\pi }{7}}\sin \left({\frac {j\pi }{7}}\right),\,1,\,0\right),$
$\left(2\cos {\frac {\pi }{7}}\cos \left({\frac {j\pi }{7}}\right),\,\pm 2\cos {\frac {\pi }{7}}\sin \left({\frac {j\pi }{7}}\right),\,\cos \left({\frac {k\pi }{7}}\right),\,\pm \sin \left({\frac {k\pi }{7}}\right)\right),$