Square-enneagrammic duoprism

Square-enneagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sastedip
Coxeter diagram	x4o x9/2o ()
Elements
Cells	9 cubes, 4 enneagrammic prisms
Faces	9+36 squares, 4 enneagrammic prisms
Edges	36+36
Vertices	36
Vertex figure	Digonal disphenoid, edge lengths 2cos(2π/9) (base 1) and √2 (base 2 and sides)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {2+{\frac {1}{\sin ^{2}{\frac {2\pi }{9}}}}}}{2}}\approx 1.05122$
Hypervolume	${\frac {9}{4\tan {\frac {2\pi }{9}}}}\approx 2.68145$
Dichoral angles	Cube–4–cube: 100°
	Step–9/2–step: 90°
	Cube–4–step: 90°
Height	1
Central density	2
Number of external pieces	22
Level of complexity	12
Related polytopes
Army	Semi-uniform sendip
Regiment	Sastedip
Dual	Square-enneagrammic duotegum
Conjugates	Square-enneagonal duoprism, Square-great enneagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B2×I2(9), order 144
Convex	No
Nature	Tame

The square-enneagrammic duoprism, also known as sastedip or the 4-9/2 duoprism, is a uniform duoprism that consists of 9 cubes and 4 enneagrammic prisms, with 2 of each at each vertex.

The name can also refer to the square-great enneagrammic duoprism, which uses a different stellation of the enneagon.

Vertex coordinates

The coordinates of a square-enneagrammic duoprism, centered at the origin and with edge length 2sin(2π/9), are given by:

• $\left(\pm \sin {\frac {2\pi }{9}},\,\pm \sin {\frac {2\pi }{9}},\,1,\,0\right),$
• $\left(\pm \sin {\frac {2\pi }{9}},\,\pm \sin {\frac {2\pi }{9}},\,\cos \left({\frac {j\pi }{9}}\right),\,\pm \sin \left({\frac {j\pi }{9}}\right)\right),$
• $\left(\pm \sin {\frac {2\pi }{9}},\,\pm \sin {\frac {2\pi }{9}},\,-{\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}}\right),$

where j = 2, 4, 8.

Representations

A square-enneagrammic duoprism has the following Coxeter diagrams:

• x4o x9/2o (full symmetry)
• x x x9/2o () (I₂(9)×A₁×A₁ symmetry, enneagrammic prismatic prism)

External links

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

• Klitzing, Richard. "nd-mb-dip".