# Heptagrammic duoprism

Heptagrammic duoprism
Rank4
TypeUniform
Notation
Bowers style acronymShedip
Coxeter diagramx7/2o x7/2o ()
Elements
Cells14 heptagrammic prisms
Faces49 squares, 14 heptagrams
Edges98
Vertices49
Vertex figureTetragonal disphenoid, edge lengths 2cos(2π/7) (bases) and 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {2}}{2\sin {\frac {2\pi }{7}}}}\approx 0.90442}$
Inradius${\displaystyle {\frac {1}{2\tan {\frac {2\pi }{7}}}}\approx 0.39874}$
Hypervolume${\displaystyle {\frac {49}{16\tan ^{2}{\frac {2\pi }{7}}}}\approx 1.94764}$
Dichoral anglesShip–4–ship: 90°
Ship–7/2–ship: ${\displaystyle {\frac {3\pi }{7}}\approx 77.14286^{\circ }}$
Central density4
Number of external pieces28
Level of complexity12
Related polytopes
ArmyHedip
RegimentShedip
DualHeptagrammic duotegum
ConjugatesHeptagonal duoprism, Great heptagrammic duoprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(7)≀S2, order 392
ConvexNo
NatureTame

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:

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

where j, k = 2, 4, 6.