Octagrammic-dodecagonal duoprism

Octagrammic-dodecagonal duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Stotwadip
Coxeter diagram	x8/3o x12o ()
Elements
Cells	12 octagrammic prisms, 8 dodecagonal prisms
Faces	96 squares, 12 octagrams, 8 dodecagons
Edges	96+96
Vertices	96
Vertex figure	Digonal disphenoid, edge lengths √2–√2 (base 1), (√6+√2)/2 (base 2), √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {6-{\sqrt {2}}+2{\sqrt {3}}}{2}}}\approx 2.00623$
Hypervolume	$6{\sqrt {6}}+12{\sqrt {2}}-6{\sqrt {3}}-12\approx 9.27520$
Dichoral angles	Stop–8/3–stop: 150°
	Stop–4–twip: 90°
	Twip–12–twip: 45°
Central density	3
Number of external pieces	28
Level of complexity	12
Related polytopes
Army	Semi-uniform otwadip
Dual	Octagrammic-dodecagonal duotegum
Conjugates	Octagonal-dodecagonal duoprism, Octagonal-dodecagrammic duoprism, Octagrammic-dodecagrammic duoprism
Abstract & topological properties
Flag count	2304
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(8)×I2(12), order 384
Convex	No
Nature	Tame

The octagrammic-dodecagonal duoprism, also known as stotwadip or the 8/3-12 duoprism, is a uniform duoprism that consists of 12 octagrammic prisms and 8 dodecagonal prisms, with 2 of each at each vertex.

Vertex coordinates

The coordinates of an octagrammic-dodecagonal duoprism, centered at the origin and with unit edge length, are given by:

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

Representations

An octagrammic-dodecagonal duoprism has the following Coxeter diagrams:

• x8/3o x12o () (full symmetry)
• x6x x8/3o () (G₂×I₂(8) symmetry, dodecagons as dihexagons)
• x4/3x x12o () (B₂×G₂(12) symmetry, octagrams as ditetragrams)
• x4/3x x6x () (B₂×G₂ symmetry)

External links

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

• Klitzing, Richard. "nd-mb-dip".