Pentagrammic tegum

Pentagrammic tegum
Rank	3
Space	Spherical
Notation
Coxeter diagram
Elements
Faces	10 isosceles triangles
Edges	5 + 10
Vertices	7
Vertex figure	5 squares + 2 pentagrams
Measures (edge length 1)
Central density	2
Related polytopes
Dual	Pentagrammic prism
Convex hull	Non-uniform pentagonal tegum
Abstract properties
Euler characteristic	2
Topological properties
Orientable	Yes
Genus	0
Properties
Convex	No
Discovered by	{{{discoverer}}}

The pentagrammic tegum is a star polyhedron. It can be constructed as the dual of the pentagrammic prism or as the tegum product of the pentagram and a line segment.

Vertex coordinates

A pentagrammic tegum of edge length 1 has the following vertices:

• $\left(±\frac{1}{2},\, -\sqrt{\frac{5-2\sqrt{5}}{20}},\,0\right),$
• $\left(±\frac{\sqrt{5}-1}{4},\, \sqrt{\frac{5+\sqrt{5}}{40}},\,0\right),$
• $\left(0,\, \sqrt{\frac{5-\sqrt{5}}{10}},\,0\right),$
• $\left(0,\,0,\,±\sqrt{\frac{5+\sqrt5}{10}}\right).$