# Pentagrammic tegum

Pentagrammic tegum
Rank3
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 & topological properties
Euler characteristic2
OrientableYes
Genus0
Properties
ConvexNo

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:

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