Great heptagrammic duoprism

Great heptagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Gishdip
Coxeter diagram	x7/3o x7/3o ()
Elements
Cells	14 great heptagrammic prisms
Faces	49 squares, 14 great heptagrams
Edges	98
Vertices	49
Vertex figure	Tetragonal disphenoid, edge lengths 2cos(3π/7) (bases) and √2 (sides)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {2}}{2\sin {\frac {3\pi }{7}}}}\approx 0.72529$
Inradius	${\frac {1}{2\tan {\frac {3\pi }{7}}}}\approx 0.11412$
Hypervolume	${\frac {49}{16\tan ^{2}{\frac {3\pi }{7}}}}\approx 0.15954$
Dichoral angles	Ship–4–ship: 90°
	Ship–7/3–ship: ${\frac {\pi }{7}}\approx 25.71429^{\circ }$
Central density	9
Number of external pieces	28
Level of complexity	12
Related polytopes
Army	Hedip
Regiment	Gishdip
Dual	Great heptagrammic duotegum
Conjugates	Heptagonal duoprism, Heptagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(7)≀S2, order 392
Convex	No
Nature	Tame

The great heptagrammic duoprism or gishdip, also known as the great heptagrammic-great heptagrammic duoprism, the 7/3 duoprism or the 7/3-7/3 duoprism, is a noble uniform duoprism that consists of 14 great heptagrammic prisms, with 4 meeting at each vertex.

Vertex coordinates

The coordinates of a great heptagrammic duoprism, centered at the origin and with edge length 2sin(3π/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".