Great enneagrammic-dodecagonal duoprism

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Great enneagrammic-dodecagonal duoprism
Rank4
TypeUniform
Notation
Coxeter diagramx9/4o x12o ()
Elements
Cells12 great enneagrammic prisms, 9 dodecagonal prisms
Faces108 squares, 12 great enneagrams, 9 dodecagons
Edges108+108
Vertices108
Vertex figureDigonal disphenoid, edge lengths 2cos(4π/9) (base 1), (6+2)/2 (base 2), 2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesGistep–9/4–gistep: 150°
 Gistep–4–twip: 90°
 Twip–12–twip: 20°
Central density4
Number of external pieces30
Level of complexity12
Related polytopes
ArmySemi-uniform etwadip
DualGreat enneagrammic-dodecagonal duotegum
ConjugatesEnneagonal-dodecagonal duoprism, Enneagonal-dodecagrammic duoprism, Enneagrammic-dodecagonal duoprism, Enneagrammic-dodecagrammic duoprism, Great enneagrammic-dodecagrammic duoprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(9)×I2(12), order 432
ConvexNo
NatureTame

The great enneagrammic-dodecagonal duoprism, also known as the 9/4-12 duoprism, is a uniform duoprism that consists of 12 great enneagrammic prisms and 9 dodecagonal prisms, with 2 of each at each vertex.

Vertex coordinates[edit | edit source]

The coordinates of a great enneagrammic-dodecagonal duoprism, centered at the origin and with edge length 2sin(4π/9), are given by:

where j = 2, 4, 8.

Representations[edit | edit source]

A great enneagrammic-dodecagonal duoprism has the following Coxeter diagrams:

External links[edit | edit source]