# Dodecagrammic prism

Dodecagrammic prism
Rank3
TypeUniform
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${\displaystyle {\frac {\sqrt {9-4{\sqrt {3}}}}{2}}\approx 0.71969}$
Volume${\displaystyle 3(2-{\sqrt {3}})\approx 0.80385}$
Dihedral angles4–12/5: 90°
4–4: 30°
Height1
Central density5
Number of external pieces26
Level of complexity6
Related polytopes
ArmySemi-uniform Twip, edge lengths ${\displaystyle 2-{\sqrt {3}}}$ (base), 1 (sides)
RegimentStwip
DualDodecagrammic tegum
ConjugateDodecagonal prism
Convex coreDodecagonal prism
Abstract & topological properties
Flag count144
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:

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