# Pentagrammic tegum

Pentagrammic tegum
Rank3
SpaceSpherical
Notation
Coxeter diagram
Elements
Faces10 isosceles triangles
Edges5 + 10
Vertices7
Vertex figure5 squares + 2 pentagrams
Measures (edge length 1)
Central density2
Related polytopes
DualPentagrammic prism
Convex hullNon-uniform pentagonal tegum
Abstract properties
Euler characteristic2
Topological properties
OrientableYes
Genus0
Properties
ConvexNo
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:

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