Heptagonal duoprism

Heptagonal duoprism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Hedip
Coxeter diagram	x7o x7o ()
Elements
Cells	14 heptagonal prisms
Faces	49 squares, 14 heptagons
Edges	98
Vertices	49
Vertex figure	Tetragonal 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 angles	Hep–7–hep: $\frac{5\pi}{7} ≈ 128.57143°$
	Hep–4–hep: 90°
Central density	1
Number of external pieces	14
Level of complexity	3
Related polytopes
Army	Hedip
Regiment	Hedip
Dual	Heptagonal duotegum
Conjugates	Heptagrammic duoprism, Great heptagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(7)≀S2, order 392
Convex	Yes
Nature	Tame

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.

Gallery

• 

  Wireframe, cell, net

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.

External links

• Bowers, Jonathan. "Category A: Duoprisms".

• Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".

• Klitzing, Richard. "hedip".