Square-dodecagrammic duoprism

Square-dodecagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Coxeter diagram	x4o2x12/5o ()
Elements
Cells	12 cubes, 4 dodecagrammic prisms
Faces	12+48 squares, 4 dodecagrams
Edges	48+48
Vertices	48
Vertex figure	Digonal disphenoid, edge lengths (√6–√2)/2 (base 1) and √2 (base 2 and sides)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{5-2\sqrt3}2} \approx 0.87633$
Hypervolume	$3(2\sqrt3) \approx 0.80385$
Dichoral angles	Stwip–12/5–stwip: 90°
	Cube–4–stwip: 90°
	Cube–4–cube: 30°
Height	1
Central density	5
Number of external pieces	28
Level of complexity	12
Related polytopes
Army	Semi-uniform sitwadip
Dual	Square-dodecagrammic duotegum
Conjugate	Square-dodecagonal duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B2×I2(12), order 192
Convex	No
Nature	Tame

The square-dodecagrammic duoprism, also known as the 4-12/5 duoprism, is a uniform duoprism that consists of 12 cubes and 4 dodecagrammic prisms, with 2 of each at each vertex.

Vertex coordinates

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

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

Representations

A square-dodecagrammic duoprism has the following Coxeter diagrams:

• x4o x12/5o () (full symmetry)
• x x x12/5o () (I₂(12)×A₁×A₁ symmetry, dodecagrammic prismatic prism)
• x4o x6/5x () (B₂×G₂ symmetry)
• x x x6/5x () (G₂×A₁×A₁ symmetry)

External links

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

• Klitzing, Richard. "nd-mb-dip".