Great enneagrammic-decagonal duoprism

Great enneagrammic-decagonal duoprism
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Gistdedip
Coxeter diagram	x9/4o x10o ()
Elements
Cells	10 great enneagrammic prisms, 9 decagonal prisms
Faces	90 squares, 10 great enneagrams, 9 decagons
Edges	90+90
Vertices	90
Vertex figure	Digonal disphenoid, edge lengths 2cos(4π/9) (base 1), √(5+√5)/2 (base 2), √2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Gistep–9/4–gistep: 144°
	Gistep–4–dip: 90°
	Dip–10–dip: 20°
Central density	4
Number of external pieces	28
Level of complexity	12
Related polytopes
Army	Semi-uniform edidip
Regiment	Gistdedip
Dual	Great enneagrammic-decagonal duotegum
Conjugates	Enneagonal-decagonal duoprism, Enneagonal-decagrammic duoprism, Enneagrammic-decagonal duoprism, Enneagrammic-decagrammic duoprism, Great enneagrammic-decagrammic duoprism
Abstract & topological properties
Flag count	1920
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(9)×I2(10), order 360
Convex	No
Nature	Tame

The great enneagrammic-decagonal duoprism, also known as gistdedip or the 9/4-10 duoprism, is a uniform duoprism that consists of 10 great enneagrammic prisms and 9 decagonal prisms, with 2 of each at each vertex.

Vertex coordinates[edit | edit source]

The coordinates of a great enneagrammic-decagonal duoprism, centered at the origin and with edge length 2sin(4π/9), are given by:

$\left(1,\,0,\,\pm \sin {\frac {4\pi }{9}},\,\pm {\sqrt {5+2{\sqrt {5}}}}\sin {\frac {4\pi }{9}}\right)$ ,
$\left(1,\,0,\,\pm {\frac {3+{\sqrt {5}}}{2}}\sin {\frac {4\pi }{9}},\,\pm {\sqrt {\frac {5+{\sqrt {5}}}{2}}}\sin {\frac {4\pi }{9}}\right)$ ,
$\left(1,\,0,\,\pm \left(1+{\sqrt {5}}\right)\sin {\frac {4\pi }{9}},\,0\right)$ ,
$\left(\cos \left({\frac {j\pi }{9}}\right),\,\pm \sin \left({\frac {j\pi }{9}}\right),\,\pm \sin {\frac {4\pi }{9}},\,\pm {\sqrt {5+2{\sqrt {5}}}}\sin {\frac {4\pi }{9}}\right)$ ,
$\left(\cos \left({\frac {j\pi }{9}}\right),\,\pm \sin \left({\frac {j\pi }{9}}\right),\,\pm {\frac {3+{\sqrt {5}}}{2}}\sin {\frac {4\pi }{9}},\,\pm {\sqrt {\frac {5+{\sqrt {5}}}{2}}}\sin {\frac {4\pi }{9}}\right)$ ,
$\left(\cos \left({\frac {j\pi }{9}}\right),\,\pm \sin \left({\frac {j\pi }{9}}\right),\,\pm \left(1+{\sqrt {5}}\right)\sin {\frac {4\pi }{9}},\,0\right)$ ,
$\left(-{\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,\pm \sin {\frac {4\pi }{9}},\,\pm {\sqrt {5+2{\sqrt {5}}}}\sin {\frac {4\pi }{9}}\right)$ ,
$\left(-{\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,\pm {\frac {3+{\sqrt {5}}}{2}}\sin {\frac {4\pi }{9}},\,\pm {\sqrt {\frac {5+{\sqrt {5}}}{2}}}\sin {\frac {4\pi }{9}}\right)$ ,
$\left(-{\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,\pm \left(1+{\sqrt {5}}\right)\sin {\frac {4\pi }{9}},\,0\right)$ ,