# Dodecagrammic duoprism

Dodecagrammic duoprism
Rank4
TypeUniform
Notation
Coxeter diagramx12/5o x12/5o ()
Elements
Cells24 dodecagrammic prisms
Faces144 squares, 24 dodecagrams
Edges288
Vertices144
Vertex figureTetragonal disphenoid, edge lengths (62)/2 (bases) and 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {3}}-1\approx 0.73205}$
Inradius${\displaystyle {\frac {2-{\sqrt {3}}}{2}}\approx 0.13397}$
Hypervolume${\displaystyle 9(7-4{\sqrt {3}})\approx 0.64617}$
Dichoral anglesStwip–4–stwip: 90°
Stwip–12/5–stwip: 30°
Central density25
Number of external pieces48
Level of complexity12
Related polytopes
DualDodecagrammic duotegum
ConjugateDodecagonal duoprism
Abstract & topological properties
Flag count3456
Euler characteristic0
OrientableYes
Properties
SymmetryI2(12)≀S2, order 1152
ConvexNo
NatureTame

The dodecagrammic duoprism, also known as the dodecagrammic-dodecagrammic duoprism, the 12/5 duoprism or the 12/5-12/5 duoprism, is a noble uniform duoprism that consists of 24 dodecagrammic prisms, with 4 at each vertex.

## Vertex coordinates

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

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

## Representations

A dodecagrammic duoprism has the following Coxeter diagrams: