Heptagrammic duoprism

Heptagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Shedip
Coxeter diagram	x7/2o x7/2o ()
Elements
Cells	14 heptagrammic prisms
Faces	49 squares, 14 heptagrams
Edges	98
Vertices	49
Vertex figure	Tetragonal disphenoid, edge lengths 2cos(2π/7) (bases) and √2 (sides)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {2}}{2\sin {\frac {2\pi }{7}}}}\approx 0.90442$
Inradius	${\frac {1}{2\tan {\frac {2\pi }{7}}}}\approx 0.39874$
Hypervolume	${\frac {49}{16\tan ^{2}{\frac {2\pi }{7}}}}\approx 1.94764$
Dichoral angles	Ship–4–ship: 90°
	Ship–7/2–ship: ${\frac {3\pi }{7}}\approx 77.14286^{\circ }$
Central density	4
Number of external pieces	28
Level of complexity	12
Related polytopes
Army	Hedip
Regiment	Shedip
Dual	Heptagrammic duotegum
Conjugates	Heptagonal duoprism, Great heptagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(7)≀S2, order 392
Convex	No
Nature	Tame

The heptagrammic duoprism or shedip, also known as the heptagrammic-heptagrammic duoprism, the 7/2 duoprism or the 7/2-7/2 duoprism, is a noble uniform duoprism that consists of 14 heptagrammic prisms, with 4 meeting at each vertex.

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

Vertex coordinates

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

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

where j, k = 2, 4, 6.

External links

• Bowers, Jonathan. "Category A: Duoprisms".

• Klitzing, Richard. "nd-mb-dip".