# Dodecagrammic prism

Dodecagrammic prism Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymStwip
Coxeter diagramx x12/5o (       )
Elements
Faces12 squares, 2 dodecagrams
Edges12+24
Vertices24
Vertex figureIsosceles triangle, edge lengths 2, 2, 2–3
Measures (edge length 1)
Circumradius$\frac{\sqrt{9-4\sqrt3}}{2} ≈ 0.71969$ Volume$3(2-\sqrt3) ≈ 0.80385$ Dihedral angles4–12/5: 90°
4–4: 30°
Height1
Central density5
Number of external pieces26
Level of complexity6
Related polytopes
ArmySemi-uniform Twip
RegimentStwip
DualDodecagrammic tegum
ConjugateDodecagonal prism
Convex coreDodecagonal prism
Abstract & topological properties
Euler characteristic2
OrientableYes
Genus0
Properties
SymmetryI2(12)×A1, order 48
ConvexNo
NatureTame

The dodecagrammic prism or stwip is a prismatic uniform polyhedron. It consists of 2 dodecagrams and 12 squares. Each vertex joins one dodecagram and two squares. As the name suggests, it is a prism based on a dodecagram.

## Vertex coordinates

A dodecagrammic prism of edge length 1 has vertex coordinates given by:

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