Heptagonal duoprism

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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
Inradius
Hypervolume
Dichoral anglesHep–7–hep:
 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.

Gallery[edit | edit source]

Vertex coordinates[edit | edit source]

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

  • ,
  • ,
  • ,
  • ,

where j, k = 2, 4, 6.

External links[edit | edit source]