Great heptagrammic prism

Great heptagrammic prism
(3D model) (OFF file)
Rank	3
Type	Uniform
Notation
Bowers style acronym	Giship
Coxeter diagram	x x7/3o ()
Elements
Faces	7 squares, 2 great heptagrams
Edges	7+14
Vertices	14
Vertex figure	Isosceles triangle, edge lengths √2, √2, 2cos(3π/7)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {1+{\frac {1}{\sin ^{2}{\frac {3\pi }{7}}}}}}{2}}\approx 0.71626$
Volume	${\frac {7}{4\tan {\frac {3\pi }{7}}}}\approx 0.39943$
Dihedral angles	4–7/3: 90°
	4–4: ${\frac {\pi }{7}}\approx 25.71429^{\circ }$
Height	1
Central density	3
Number of external pieces	16
Level of complexity	6
Related polytopes
Army	Semi-uniform Hep, edge lengths $2\cos {\frac {3\pi }{7}}$ (base), 1 (sides)
Regiment	Giship
Dual	Great heptagrammic tegum
Conjugates	Heptagonal prism, Heptagrammic prism
Convex core	Heptagonal prism
Abstract & topological properties
Flag count	84
Euler characteristic	2
Orientable	Yes
Genus	0
Properties
Symmetry	I2(7)×A1, order 28
Convex	No
Nature	Tame

The great heptagrammic prism, or giship, is a prismatic uniform polyhedron. It consists of 2 great heptagrams and 7 squares. Each vertex joins one great heptagram and two squares. As the name suggests, it is a prism based on a great heptagram.

Vertex coordinates

The coordinates of a great heptagrammic prism, centered at the origin and with edge length 2sin(3π/7), are given by:

• (1, 0, ±sin(3π/7)),
• (cos(2π/7), ±sin(2π/7), ±sin(3π/7)),
• (cos(4π/7), ±sin(4π/7), ±sin(3π/7)),
• (cos(6π/7), ±sin(6π/7), ±sin(3π/7)).

External links

• Klitzing, Richard. "giship".
• Wikipedia contributors. "Heptagrammic prism (7/3)".
• McCooey, David. "Heptagrammic 7/3 Prism"