Square-heptagrammic duoprism

Square-heptagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sashedip
Coxeter diagram	x4o x7/2o ()
Elements
Cells	7 cubes, 4 heptagrammic prisms
Faces	7+28 squares, 4 heptagrams
Edges	28+28
Vertices	28
Vertex figure	Digonal disphenoid, 2cos(2π/7) (base 1) and √2 (base 2 and sides)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {2+{\frac {1}{\sin ^{2}{\frac {2\pi }{7}}}}}}{2}}\approx 0.95341$
Hypervolume	${\frac {7}{4\tan {\frac {2\pi }{7}}}}\approx 1.39558$
Dichoral angles	Ship–7/2–ship: 90°
	Cube–4–ship: 90°
	Cube–4–cube: ${\frac {3\pi }{7}}\approx 77.14286^{\circ }$
Height	1
Central density	2
Number of external pieces	18
Level of complexity	12
Related polytopes
Army	Semi-uniform squahedip
Regiment	Sashedip
Dual	Square-heptagrammic duotegum
Conjugates	Square-heptagonal duoprism, Square-great heptagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B2×I2(7), order 112
Convex	No
Nature	Tame

The square-heptagrammic duoprism, also known as sashedip or the 4-7/2 duoprism, is a uniform duoprism that consists of 7 cubes and 4 heptagrammic prisms, with 2 of each at each vertex.

The name can also refer to the square-great heptagrammic duoprism.

Vertex coordinates

The coordinates of a square-heptagrammic duoprism, centered at the origin and with edge length 2sin(2π/7), are given by:

• $\left(\pm \sin {\frac {2\pi }{7}},\,\pm \sin {\frac {2\pi }{7}},\,1,\,0\right),$
• $\left(\pm \sin {\frac {2\pi }{7}},\,\pm \sin {\frac {2\pi }{7}},\,\cos \left({\frac {j\pi }{7}}\right),\,\pm \sin \left({\frac {j\pi }{7}}\right)\right),$

where j = 2, 4, 6.

Representations

A square-heptagrammic duoprism has the following Coxeter diagrams:

• x4o x7/2o (full symmetry)
• x x x7/2o () (I₂(7)×A₁×A₁ symmetry, heptagrammic prismatic prism)

External links

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

• Klitzing, Richard. "nd-mb-dip".