Heptagrammic-dodecagonal duoprism

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Heptagrammic-dodecagonal duoprism
Rank4
TypeUniform
Notation
Coxeter diagramx7/2o x12o ()
Elements
Cells12 heptagrammic prisms, 7 dodecagonal prisms
Faces84 squares, 12 heptagrams, 7 dodecagons
Edges84+84
Vertices84
Vertex figureDigonal disphenoid, edge lengths 2cos(2π/7) (base 1), (6+2)/2 (base 2), 2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesShip–7/2–ship: 150°
 Ship–4–twip: 90°
 Twip–12–twip:
Central density2
Number of external pieces26
Level of complexity12
Related polytopes
ArmySemi-uniform hetwadip
DualHeptagrammic-dodecagonal duotegum
ConjugatesHeptagonal-dodecagonal duoprism, Heptagonal-dodecagrammic duoprism, Heptagrammic-dodecagrammic duoprism, Great heptagrammic-dodecagonal duoprism, Great heptagrammic-dodecagrammic duoprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(7)×I2(12), order 336
ConvexNo
NatureTame

The heptagrammic-dodecagonal duoprism, also known as the 7/2-12 duoprism, is a uniform duoprism that consists of 12 heptagrammic prisms and 7 dodecagonal prisms, with 2 of each at each vertex.

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

Vertex coordinates[edit | edit source]

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

where j = 2, 4, 6.

Representations[edit | edit source]

A heptagrammic-dodecagonal duoprism has the following Coxeter diagrams:

External links[edit | edit source]