Triangular duoantifastegiaprism

Triangular duoantifastegiaprism
File:Triangular duoantifastegiaprism.png (OFF file)
Rank	5
Type	Scaliform
Notation
Bowers style acronym	Tridafup
Coxeter diagram	xo3ox xo3ox&#x
Elements
Tera	2 triangular duoprisms, 12 triangular antifastegiums
Cells	18 tetrahedra, 18 square pyramids, 12 triangular prisms, 12 octahedra
Faces	12+72 triangles, 18 squares
Edges	36+36
Vertices	18
Vertex figure	Square-tetragonal disphenoidal wedge, edge lengths 1 and √2
Measures (edge length 1)
Circumradius	${\frac {\sqrt {3}}{2}}\approx 0.86603$
Hypervolume	${\frac {9{\sqrt {3}}}{80}}\approx 0.19486$
Height	${\frac {\sqrt {3}}{3}}\approx 0.57735$
Central density	1
Related polytopes
Army	Tridafup
Regiment	Tridafup
Dual	Triangular duoantifastegiategum
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	(G2▲S2)/2, order 144
Convex	Yes
Nature	Tame

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

This polyteron also occurs as a parabidiminishing of the dodecateron, formed by removing two opposite vertices, or removing two triangular duoprismatic pyramids.

Vertex coordinates

The vertices of a triangular duoantifastegiaprism of edge length 1 are given by:

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

External links

• Klitzing, Richard. "tridafup".