Tetrahedral-antitegmatic triacontateron

Tetrahedral-antitegmatic triacontateron
(OFF file)
Rank	5
Type	Uniform dual
Notation
Coxeter diagram	m3o3o3o3m
Elements
Tera	30 tetrahedral antitegums
Cells	120 triangular antitegums
Faces	90+120 rhombi
Edges	60+120
Vertices	12+20+30
Vertex figure	12 pentachora, 30 tetrahedral tegums, 20 triangular duotegums
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Small cellidodecateron
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	A5×2, order 1440
Convex	Yes
Nature	Tame

The tetrahedral-antitegmatic triacontateron is a convex isoteric polyteron with 30 identical tetrahedral antitegums as tera. It can be obtained as the dual of the small cellidodecateron.

It can also be constructed as the convex hull of 2 dual hexatera, 2 opposite rectified hexatera, and a dodecateron, all of the same edge length.

Each face of this polyhedron is a rhombus with acute angle $\arccos \left({\frac {1}{5}}\right)\approx 78.46304^{\circ }$ and obtuse angle $\arccos \left(-{\frac {1}{5}}\right)\approx 101.53696^{\circ }$.