Triangular duoantifastegium

Triangular duoantifastegium
File:Triangular duoantifastegium.png (OFF file)
Rank	5
Type	Scaliform
Notation
Bowers style acronym	Triddaf
Coxeter diagram	xo ox xo3ox&#x
Elements
Tera	6 square scalenes, 4 triangular antifastegiums
Cells	6+12 tetrahedra, 12 square pyramids, 2 triangular prisms, 4 octahedra
Faces	4+24+24 triangles, 6 squares
Edges	6+12+24
Vertices	12
Vertex figure	Skewed triangular prismatic pyramid, base edge length 1, lacing edge lengths 1 and √2
Measures (edge length 1)
Circumradius	${\frac {\sqrt {10}}{4}}\approx 0.79057$
Hypervolume	${\frac {7{\sqrt {2}}}{240}}\approx 0.041248$
Height	${\frac {\sqrt {6}}{6}}\approx 0.40825$
Central density	1
Related polytopes
Army	Triddaf
Regiment	Triddaf
Dual	Digonal-triangular duoantifastegiategum
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	(B2▲G2)/2, order 48
Convex	Yes
Nature	Tame

The triangular duoantifastegium or triddaf, also known as the digonal-triangular duoantifastegiaprism, digonal-triangular duoantiwedge, is a convex scaliform polyteron and the first member of the duoantifastegium family. It consists of 4 triangular antifastegiums and 6 square scalenes, with 3 of each joining at each vertex.

It can be obtained as a diminishing of the demipenteract, by removing the vertices of 2 opposite edges.

Vertex coordinates

Coordinates for the vertices of a triangular duoantifastegium of edge length 1, centered at the origin, are given by:

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

External links

• Klitzing, Richard. "triddaf".