Heptagonal-heptagrammic duoprism

From Polytope Wiki
(Redirected from 7-7/2 duoprism)
Jump to navigation Jump to search
Heptagonal-heptagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymHeshedip
Info
Coxeter diagramx7o x7/2o
SymmetryI2(7)×I2(7), order 196
ArmySemi-uniform hedip
RegimentHeshedip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(π/7) (base 1), 2cos(2π/7) (base 2), 2 (sides)
Cells7 heptagonal prisms, 7 heptagrammic prisms
Faces49 squares, 7 heptagons, 7 heptagrams
Edges49+49
Vertices49
Measures (edge length 1)
Circumradius
Hypervolume49/32*[cot2(π/7)–1] ≈ 5.07141
Dichoral anglesHep–7–hep: 3π/7 ≈ 77.14286°
 Ship–7/2–ship: 5π/7 ≈ 128.57143°
 Hep–4–ship: 90°
Central density2
Related polytopes
DualHeptagonal-heptagrammic duotegum
ConjugatesHeptagonal-great heptagrammic duoprism, Heptagrammic-great heptagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame


The heptagonal-heptagrammic duoprism, also known as heshedip or the 7-7/2 duoprism, is a uniform duoprism that consists of 7 heptagonal prisms and 7 heptagrammic prisms, with 2 of each meeting at each vertex.

The name can also refer to the heptagonal-great heptagrammic duoprism.

Vertex coordinates[edit | edit source]

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

  • (2cos(π/7), 0, 1, 0),
  • (2cos(π/7), 0, cos(2π/7), ±sin(2π/7)),
  • (2cos(π/7), 0, cos(4π/7), ±sin(4π/7)),
  • (2cos(π/7), 0, cos(6π/7), ±sin(6π/7)),
  • (2cos(π/7)cos(2π/7), ±2sin(2π/7)cos(π/7), 1, 0),
  • (2cos(π/7)cos(2π/7), ±2sin(2π/7)cos(π/7), cos(2π/7), ±sin(2π/7)),
  • (2cos(π/7)cos(2π/7), ±2sin(2π/7)cos(π/7), cos(4π/7), ±sin(4π/7)),
  • (2cos(π/7)cos(2π/7), ±2sin(2π/7)cos(π/7), cos(6π/7), ±sin(6π/7)),
  • (2cos(π/7)cos(4π/7), ±2sin(4π/7)cos(π/7), 1, 0),
  • (2cos(π/7)cos(4π/7), ±2sin(4π/7)cos(π/7), cos(2π/7), ±sin(2π/7)),
  • (2cos(π/7)cos(4π/7), ±2sin(4π/7)cos(π/7), cos(4π/7), ±sin(4π/7)),
  • (2cos(π/7)cos(4π/7), ±2sin(4π/7)cos(π/7), cos(6π/7), ±sin(6π/7)),
  • (2cos(π/7)cos(6π/7), ±2sin(6π/7)cos(π/7), 1, 0),
  • (2cos(π/7)cos(6π/7), ±2sin(6π/7)cos(π/7), cos(2π/7), ±sin(2π/7)),
  • (2cos(π/7)cos(6π/7), ±2sin(6π/7)cos(π/7), cos(4π/7), ±sin(4π/7)),
  • (2cos(π/7)cos(6π/7), ±2sin(6π/7)cos(π/7), cos(6π/7), ±sin(6π/7)).

External links[edit | edit source]