# Dodecagrammic duoprism

Dodecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
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$\sqrt3-1 ≈ 0.73205$ Inradius$\frac{2-\sqrt3}{2} ≈ 0.13397$ Hypervolume$9(7-4\sqrt3) ≈ 0.64617$ 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
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:

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

A dodecagrammic duoprism has the following Coxeter diagrams:

• x12/5o x12/5o (full symmetry)
• x6/5x x12/5o (           ) (G2×I2(12) symmetry)
• x6/5x x6/5x (           ) (G2≀S2 symmetry)