# Dodecagonal-dodecagrammic duoprism

Dodecagonal-dodecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
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
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 an dodecagonal-dodecagrammic duoprism, centered at the origin and with unit edge length, are given by:

• ${\displaystyle \left(±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{\sqrt3-1}{2},\,±\frac{\sqrt3-1}{2}\right),}$
• ${\displaystyle \left(±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac12,\,±\frac{2-\sqrt3}{2}\right),}$
• ${\displaystyle \left(±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{2-\sqrt3}{2},\,±\frac12\right),}$
• ${\displaystyle \left(±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac{\sqrt3-1}{2},\,±\frac{\sqrt3-1}{2}\right),}$
• ${\displaystyle \left(±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{2-\sqrt3}{2}\right),}$
• ${\displaystyle \left(±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac{2-\sqrt3}{2},\,±\frac12\right),}$
• ${\displaystyle \left(±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{\sqrt3-1}{2},\,±\frac{\sqrt3-1}{2}\right),}$
• ${\displaystyle \left(±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac12,\,±\frac{2-\sqrt3}{2}\right),}$
• ${\displaystyle \left(±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{2-\sqrt3}{2},\,±\frac12\right).}$

## Representations

A dodecagonal-dodecagrammic duoprism has the following Coxeter diagrams: