Hexagonal-heptagonal duoprism

Hexagonal-heptagonal duoprism
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Hahedip
Coxeter diagram	x6o x7o ()
Elements
Cells	7 hexagonal prisms, 6 heptagonal prisms
Faces	42 squares, 7 hexagons, 6 heptagons
Edges	42+42
Vertices	42
Vertex figure	Digonal disphenoid, edge lengths √3 (base 1), 2cos(π/7) (base 2), and √2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Hip–6–hip:
	Hep–7–hep: 120°
	Hip–4–hep: 90°
Central density	1
Number of external pieces	13
Level of complexity	6
Related polytopes
Army	Hahedip
Regiment	Hahedip
Dual	Hexagonal-heptagonal duotegum
Conjugates	Hexagonal-heptagrammic duoprism, Hexagonal-great heptagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	G2×I2(7), order 168
Convex	Yes
Nature	Tame

The hexagonal-heptagonal duoprism or hahedip, also known as the 6-7 duoprism, is a uniform duoprism that consists of 6 heptagonal prisms and 7 hexagonal prisms, with two of each joining at each vertex.

Vertex coordinates[edit | edit source]

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

$\left(\pm 2\sin {\frac {\pi }{7}},0,1,0\right),$
$\left(\pm 2\sin {\frac {\pi }{7}},0,\cos \left({\frac {j\pi }{7}}\right),\pm \sin \left({\frac {j\pi }{7}}\right)\right),$
$\left(\pm \sin {\frac {\pi }{7}},\pm {\sqrt {3}}\sin {\frac {\pi }{7}},1,0\right),$
$\left(\pm \sin {\frac {\pi }{7}},\pm {\sqrt {3}}\sin {\frac {\pi }{7}},\cos \left({\frac {j\pi }{7}}\right),\pm \sin \left({\frac {j\pi }{7}}\right)\right),$