# Heptagonal duoprism

Heptagonal duoprism
Rank4
TypeUniform
Notation
Bowers style acronymHedip
Coxeter diagramx7o x7o ()
Elements
Cells14 heptagonal prisms
Faces49 squares, 14 heptagons
Edges98
Vertices49
Vertex figureTetragonal disphenoid, edge lengths 2cos(π/7) (bases) and 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {2}}{2\sin {\frac {\pi }{7}}}}\approx 1.62971}$
Inradius${\displaystyle {\frac {1}{2\tan {\frac {\pi }{7}}}}\approx 1.03826}$
Hypervolume${\displaystyle {\frac {49}{16\tan ^{2}{\frac {\pi }{7}}}}\approx 13.20532}$
Dichoral anglesHep–7–hep: ${\displaystyle {\frac {5\pi }{7}}\approx 128.57143^{\circ }}$
Hep–4–hep: 90°
Central density1
Number of external pieces14
Level of complexity3
Related polytopes
ArmyHedip
RegimentHedip
DualHeptagonal duotegum
ConjugatesHeptagrammic duoprism,
Great heptagrammic duoprism
Abstract & topological properties
Flag count1176
Euler characteristic0
OrientableYes
Properties
SymmetryI2(7)≀S2, order 392
Flag orbits3
ConvexYes
NatureTame

The heptagonal duoprism or hedip, also known as the heptagonal-heptagonal duoprism, the 7 duoprism or the 7-7 duoprism, is a noble uniform duoprism that consists of 14 heptagonal prisms, with 4 joining at each vertex. It is also the 14-6 gyrochoron. It is the first in an infinite family of isogonal heptagonal dihedral swirlchora and also the first in an infinite family of isochoric heptagonal hosohedral swirlchora.

## Vertex coordinates

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

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

where j, k = 2, 4, 6.