Dodecagrammic prism

Dodecagrammic prism
(3D model) (OFF file)
Rank	3
Type	Uniform
Notation
Bowers style acronym	Stwip
Coxeter diagram	x x12/5o ()
Elements
Faces	12 squares, 2 dodecagrams
Edges	12+24
Vertices	24
Vertex figure	Isosceles triangle, edge lengths √2, √2, √2–√3
Measures (edge length 1)
Circumradius	${\frac {\sqrt {9-4{\sqrt {3}}}}{2}}\approx 0.71969$
Volume	$3(2-{\sqrt {3}})\approx 0.80385$
Dihedral angles	4–12/5: 90°
	4–4: 30°
Height	1
Central density	5
Number of external pieces	26
Level of complexity	6
Related polytopes
Army	Semi-uniform Twip, edge lengths $2-{\sqrt {3}}$ (base), 1 (sides)
Regiment	Stwip
Dual	Dodecagrammic tegum
Conjugate	Dodecagonal prism
Convex core	Dodecagonal prism
Abstract & topological properties
Flag count	144
Euler characteristic	2
Orientable	Yes
Genus	0
Properties
Symmetry	I2(12)×A1, order 48
Convex	No
Nature	Tame

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:

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

External links

• Wikipedia contributors. "Dodecagrammic prism".