Dodecagrammic duoprism

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.

Dodecagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Coxeter diagram	x12/5o x12/5o ()
Elements
Cells	24 dodecagrammic prisms
Faces	144 squares, 24 dodecagrams
Edges	288
Vertices	144
Vertex figure	Tetragonal disphenoid, edge lengths (√6–√2)/2 (bases) and √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {3}}-1\approx 0.73205$
Inradius	${\frac {2-{\sqrt {3}}}{2}}\approx 0.13397$
Hypervolume	$9(7-4{\sqrt {3}})\approx 0.64617$
Dichoral angles	Stwip–4–stwip: 90°
	Stwip–12/5–stwip: 30°
Central density	25
Number of external pieces	48
Level of complexity	12
Related polytopes
Army	Twaddip
Dual	Dodecagrammic duotegum
Conjugate	Dodecagonal duoprism
Abstract & topological properties
Flag count	3456
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(12)≀S2, order 1152
Convex	No
Nature	Tame

Vertex coordinates

The coordinates of a dodecagrammic duoprism, centered at the origin and with unit edge length, are given by:

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

Representations

A dodecagrammic duoprism has the following Coxeter diagrams:

• x12/5o x12/5o () (full symmetry)
• x6/5x x12/5o () (G₂×I₂(12) symmetry, some dodecagrams as dihexagrams)
• x6/5x x6/5x () (G₂≀S₂ symmetry, all dodecagrams as dihexagrams)

External links

• Bowers, Jonathan. "Category A: Duoprisms".

• Klitzing, Richard. "nd-mb-dip".