Square-hexagonal duoantifastegiaprism

Square-hexagonal duoantifastegiaprism
(OFF file)
Rank	5
Type	Scaliform
Notation
Bowers style acronym	Shidafup
Coxeter diagram	xo4ox xo6ox&#x
Elements
Tera	12 square antifastegiums, 8 hexagonal antifastegiums, 2 square-hexagonal duoprisms
Cells	48 tetrahedra, 48 square pyramids, 12 cubes, 12 square antiprisms, 8 hexagonal prisms, 8 hexagonal antiprisms
Faces	96+96 triangles, 12+48 squares, 8 hexagons
Edges	48+48+96
Vertices	48
Vertex figure	Square-digonal disphenoidal wedge, edge lengths 1, √2, and √3
Measures (edge length 1)
Circumradius	${\sqrt {\frac {8+{\sqrt {2}}+2{\sqrt {3}}}{8}}}\approx 1.26877$
Hypervolume	${\frac {\sqrt {32+{\frac {125{\sqrt {2}}}{2}}+97{\sqrt {3}}+56{\sqrt {6}}}}{10}}\approx 2.06293$
Height	${\sqrt {\frac {-4+{\sqrt {2}}+2{\sqrt {3}}}{2}}}\approx 0.66269$
Central density	1
Related polytopes
Army	Shidafup
Regiment	Shidafup
Dual	Square-hexagonal duoantifastegiategum
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	(I2(8)▲I2(12))/2, order 192
Convex	Yes
Nature	Tame

The square-hexagonal duoantifastegiaprism or shidafup, also known as the square-hexagonal duoantiwedge, is a convex scaliform polyteron and a member of the duoantifastegiaprism family. It consists of 2 square-hexagonal duoprisms, 8 hexagonal antifastegiums and 12 square antifastegiums. 1 square-hexagonal duoprism, 3 hexagonal antifastegiums, and 3 square antifastegiums join at each vertex.

Vertex coordinates

The vertices of a square-hexagonal duoantifastegiaprism of edge length 1 are given by:

• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm 1,\,0,\,{\sqrt {\frac {-4+{\sqrt {2}}+2{\sqrt {3}}}{8}}}\right),$
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,{\sqrt {\frac {-4+{\sqrt {2}}+2{\sqrt {3}}}{8}}}\right),$
• $\left(\pm {\frac {\sqrt {2}}{2}},\,0,\,0,\,\pm 1,\,-{\sqrt {\frac {-4+{\sqrt {2}}+2{\sqrt {3}}}{8}}}\right),$
• $\left(\pm {\frac {\sqrt {2}}{2}},\,0,\,\pm {\frac {\sqrt {3}}{2}},\,\pm {\frac {1}{2}},\,-{\sqrt {\frac {-4+{\sqrt {2}}+2{\sqrt {3}}}{8}}}\right).$
• $\left(0,\,\pm {\frac {\sqrt {2}}{2}},\,0,\,\pm 1,\,-{\sqrt {\frac {-4+{\sqrt {2}}+2{\sqrt {3}}}{8}}}\right),$
• $\left(0,\,\pm {\frac {\sqrt {2}}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,\pm {\frac {1}{2}},\,-{\sqrt {\frac {-4+{\sqrt {2}}+2{\sqrt {3}}}{8}}}\right),$