Square-enneagonal duoprism

Square-enneagonal duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sendip
Coxeter diagram	x4o x9o ()
Elements
Cells	9 cubes, 4 enneagonal prisms
Faces	9+36 squares, 4 enneagons
Edges	36+36
Vertices	36
Vertex figure	Digonal disphenoid, edge lengths 2cos(π/9) (base 1) and √2 (base 2 and sides)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {2+{\frac {1}{\sin ^{2}{\frac {\pi }{9}}}}}}{2}}\approx 1.62393$
Hypervolume	${\frac {9}{4\tan {\frac {\pi }{9}}}}\approx 6.18182$
Dichoral angles	Cube–4–cube: 140°
	Cube–4–ep: 90°
	Ep–9–ep: 90°
Height	1
Central density	1
Number of external pieces	13
Level of complexity	6
Related polytopes
Army	Sendip
Regiment	Sendip
Dual	Square-enneagonal duotegum
Conjugates	Square-enneagrammic duoprism, Square-great enneagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B2×I2(9), order 144
Convex	Yes
Nature	Tame

The square-enneagonal duoprism or sendip, also known as the 4-9 duoprism, is a uniform duoprism that consists of 4 enneagonal prisms and 9 cubes, with two of each joining at each vertex. It is also a convex segmentochoron, being the prism of the enneagonal prism.

Vertex coordinates

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

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

where j = 2, 4, 8.

Representations

A square-enneagonal duoprism has the following Coxeter diagrams:

• x4o x9o () (full symmetry)
• x x x9o () () (squares as rectangles)

External links

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

• Klitzing, Richard. "n-m-dip".