Triangular-hexagonal duoantifastegiaprism

Triangular-hexagonal duoantifastegiaprism
(OFF file)
Rank	5
Type	Scaliform
Notation
Bowers style acronym	Thidafup
Coxeter diagram	xo3ox xo6ox&#x
Elements
Tera	12 triangular antifastegiums, 6 hexagonal antifastegiums, 2 triangular-hexagonal duoprisms
Cells	36 tetrahedra, 36 square pyramids, 12 triangular prisms, 12 octahedra, 6 hexagonal prisms, 6 hexagonal antiprisms
Faces	12+72+72 triangles, 36 squares, 6 hexagons
Edges	36+36+72
Vertices	36
Vertex figure	Square-digonal disphenoidal wedge, edge lengths 1, √2, and √3
Measures (edge length 1)
Circumradius	${\frac {\sqrt {4+{\sqrt {3}}}}{2}}\approx 1.19709$
Hypervolume	${\frac {\sqrt {464+653{\sqrt {3}}}}{40}}\approx 0.99845$
Height	${\sqrt {\frac {3{\sqrt {3}}-4}{3}}}\approx 0.63144$
Central density	1
Related polytopes
Army	Thidafup
Regiment	Thidafup
Dual	Triangular-hexagonal duoantifastegiategum
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	(G2▲I2(12))/2, order 144
Convex	Yes
Nature	Tame

The triangular-hexagonal duoantifastegiaprism or thidafup, also known as the triangular-hexagonal duoantiwedge, is a convex scaliform polyteron and a member of the duoantifastegiaprism family. It consists of 2 triangular-hexagonal duoprisms, 6 hexagonal antifastegiums, and 12 triangular antifastegiums. 1 triangular-hexagonal duoprism, 3 hexagonal antifastegiums, and 3 triangular antifastegiums join at each vertex.

Vertex coordinates

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

• $\left(\pm 1,\,0,\,0,\,{\frac {\sqrt {3}}{3}},\,{\sqrt {\frac {3{\sqrt {3}}-4}{12}}}\right),$
• $\left(\pm 1,\,0,\,\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,{\sqrt {\frac {3{\sqrt {3}}-4}{12}}}\right),$
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,0,\,{\frac {\sqrt {3}}{3}},\,{\sqrt {\frac {3{\sqrt {3}}-4}{12}}}\right),$
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,{\sqrt {\frac {3{\sqrt {3}}-4}{12}}}\right),$
• $\left(0,\,\pm 1,\,0,\,-{\frac {\sqrt {3}}{3}},\,-{\sqrt {\frac {3{\sqrt {3}}-4}{12}}}\right),$
• $\left(0,\,\pm 1,\,\pm {\frac {1}{2}},\,{\frac {\sqrt {3}}{6}},\,-{\sqrt {\frac {3{\sqrt {3}}-4}{12}}}\right),$
• $\left(\pm {\frac {\sqrt {3}}{2}},\,\pm {\frac {1}{2}},\,0,\,-{\frac {\sqrt {3}}{3}},\,-{\sqrt {\frac {3{\sqrt {3}}-4}{12}}}\right),$
• $\left(\pm {\frac {\sqrt {3}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,{\frac {\sqrt {3}}{6}},\,-{\sqrt {\frac {3{\sqrt {3}}-4}{12}}}\right).$