Triangular-square duoantifastegiaprism

Triangular-square duoantifastegiaprism
(OFF file)
Rank	5
Type	Scaliform
Notation
Bowers style acronym	Tisdafup
Coxeter diagram	xo3ox xo4ox&#x
Elements
Tera	8 triangular antifastegiums, 6 square antifastegiums, 2 triangular-square duoprisms
Cells	24 tetrahedra, 24 square pyramids, 8 triangular prisms, 8 octahedra, 6 cubes, 6 square antiprisms
Faces	8+48+48 triangles, 6+24 squares
Edges	24+24+48
Vertices	24
Vertex figure	Square-digonal disphenoidal wedge, edge lengths 1 and √2
Measures (edge length 1)
Circumradius	${\frac {\sqrt {12+2{\sqrt {2}}}}{4}}\approx 0.96269$
Hypervolume	${\frac {\sqrt {1116+874{\sqrt {2}}}}{120}}\approx 0.40415$
Height	${\sqrt {\frac {3{\sqrt {2}}-2}{6}}}\approx 0.61137$
Central density	1
Related polytopes
Army	Tisdafup
Regiment	Tisdafup
Dual	Triangular-square duoantifastegiategum
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	(G2▲I2(8))/2, order 96
Convex	Yes
Nature	Tame

The triangular-square duoantifastegiaprism or tisdafup, also known as the triangular-square duoantiwedge, is a convex scaliform polyteron and a member of the duoantifastegiaprism family. It consists of 2 triangular-square duoprisms, 6 square antifastegiums, and 8 triangular antifastegiums. 1 triangular-square duoprism, 3 square antifastegiums, and 3 triangular antifastegiums join at each vertex.

Vertex coordinates

A triangular-square duoantifastegiaprism of edge length 1 has vertex coordinates given by:

• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,{\frac {\sqrt {3}}{3}},\,{\sqrt {\frac {3{\sqrt {2}}-2}{24}}}\right),$
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,{\sqrt {\frac {3{\sqrt {2}}-2}{24}}}\right),$
• $\left(0,\,\pm {\frac {\sqrt {2}}{2}},\,0,\,-{\frac {\sqrt {3}}{3}},\,-{\sqrt {\frac {3{\sqrt {2}}-2}{24}}}\right),$
• $\left(0,\,\pm {\frac {\sqrt {2}}{2}},\,\pm {\frac {1}{2}},\,{\frac {\sqrt {3}}{6}},\,-{\sqrt {\frac {3{\sqrt {2}}-2}{24}}}\right),$
• $\left(\pm {\frac {\sqrt {2}}{2}},\,0,\,0,\,-{\frac {\sqrt {3}}{3}},\,-{\sqrt {\frac {3{\sqrt {2}}-2}{24}}}\right),$
• $\left(\pm {\frac {\sqrt {2}}{2}},\,0,\,\pm {\frac {1}{2}},\,{\frac {\sqrt {3}}{6}},\,-{\sqrt {\frac {3{\sqrt {2}}-2}{24}}}\right).$