# Heptagonal duoprism

Heptagonal duoprism Rank4
TypeUniform
SpaceSpherical
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$\frac{\sqrt2}{2\sin\frac\pi7} ≈ 1.62971$ Inradius$\frac{1}{2\tan\frac\pi7} ≈ 1.03826$ Hypervolume$\frac{49}{16\tan^2\frac\pi7} ≈ 13.20532$ Dichoral anglesHep–7–hep: $\frac{5\pi}{7} ≈ 128.57143°$ 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
Euler characteristic0
OrientableYes
Properties
SymmetryI2(7)≀S2, order 392
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:

• $\left(1,0,1,0\right),$ • $\left(1,0,\cos\left(\frac{j\pi}7\right),±\sin\left(\frac{j\pi}7\right)\right),$ • $\left(\cos\left(\frac{k\pi}7\right),±\sin\left(\frac{k\pi}7\right),1,0\right),$ • $\left(\cos\left(\frac{k\pi}7\right),±\sin\left(\frac{k\pi}7\right),\cos\left(\frac{j\pi}7\right),±\sin\left(\frac{j\pi}7\right)\right),$ where j, k = 2, 4, 6.