# Great heptagrammic duoprism

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Great heptagrammic duoprism
Rank4
TypeUniform
Notation
Bowers style acronymGishdip
Coxeter diagramx7/3o x7/3o ()
Elements
Cells14 great heptagrammic prisms
Faces49 squares, 14 great heptagrams
Edges98
Vertices49
Vertex figureTetragonal disphenoid, edge lengths 2cos(3π/7) (bases) and 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {2}}{2\sin {\frac {3\pi }{7}}}}\approx 0.72529}$
Inradius${\displaystyle {\frac {1}{2\tan {\frac {3\pi }{7}}}}\approx 0.11412}$
Hypervolume${\displaystyle {\frac {49}{16\tan ^{2}{\frac {3\pi }{7}}}}\approx 0.15954}$
Dichoral anglesShip–4–ship: 90°
Ship–7/3–ship: ${\displaystyle {\frac {\pi }{7}}\approx 25.71429^{\circ }}$
Central density9
Number of external pieces28
Level of complexity12
Related polytopes
ArmyHedip
RegimentGishdip
DualGreat heptagrammic duotegum
ConjugatesHeptagonal duoprism, Heptagrammic duoprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(7)≀S2, order 392
ConvexNo
NatureTame

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:

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

where j, k = 2, 4, 6.