# Dodecagonal-dodecagrammic duoprism

Dodecagonal-dodecagrammic duoprism
Rank4
TypeUniform
Notation
Coxeter diagramx12o x12/5o ()
Elements
Cells12 dodecagonal prisms, 12 dodecagrammic prisms
Faces144 squares, 12 dodecagons, 12 dodecagrams
Edges144+144
Vertices144
Vertex figureDigonal disphenoid, edge lengths (6+2)/2 (base 1), (62)/2 (base 2), 2 (sides)
Measures (edge length 1)
Hypervolume9
Dichoral anglesStwip–12/5–stwip: 150°
Twip–4–stwip: 90°
Twip–12–twip: 30°
Central density5
Number of external pieces36
Level of complexity12
Related polytopes
DualDodecagonal-dodecagrammic duotegum
ConjugateDodecagonal-dodecagrammic duoprism
Abstract & topological properties
Flag count3456
Euler characteristic0
OrientableYes
Properties
SymmetryI2(12)×I2(12), order 576
ConvexNo
NatureTame

The dodecagonal-dodecagrammic duoprism, also known as the 12/5-12 duoprism, is a uniform duoprism that consists of 12 dodecagonal prisms and 12 dodecagrammic prisms, with 2 of each at each vertex.

## Vertex coordinates

The coordinates of a dodecagonal-dodecagrammic duoprism, centered at the origin and with unit edge length, are given by:

• ${\displaystyle \left(\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {{\sqrt {3}}-1}{2}},\,\pm {\frac {{\sqrt {3}}-1}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {2-{\sqrt {3}}}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {1+{\sqrt {3}}}{2}},\,\pm {\frac {2-{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {{\sqrt {3}}-1}{2}},\,\pm {\frac {{\sqrt {3}}-1}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {2-{\sqrt {3}}}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {2-{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {3}}-1}{2}},\,\pm {\frac {{\sqrt {3}}-1}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {2-{\sqrt {3}}}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {2+{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {2-{\sqrt {3}}}{2}},\,\pm {\frac {1}{2}}\right)}$.

## Representations

A dodecagonal-dodecagrammic duoprism has the following Coxeter diagrams: