# Elongated pentagonal bipyramid

Elongated pentagonal bipyramid
Rank3
TypeCRF
Notation
Bowers style acronymEpedpy
Coxeter diagramoxxo5oooo&#xt
Elements
Faces10 triangles, 5 squares
Edges5+10+10
Vertices2+10
Vertex figures2 pentagons, edge length 1
10 kites, edge lengths 1 and 2
Measures (edge length 1)
Volume${\displaystyle {\frac {5+{\sqrt {5}}+3{\sqrt {25+1{\sqrt {5}}}}}{12}}\approx 2.32348}$
Dihedral angles3–3: ${\displaystyle \arccos \left(-{\frac {\sqrt {5}}{3}}\right)\approx 138.18969^{\circ }}$
3–4: ${\displaystyle \arccos \left(-{\sqrt {\frac {10-2{\sqrt {5}}}{15}}}\right)\approx 127.37737^{\circ }}$
4–4: 108°
Central density1
Number of external pieces15
Level of complexity5
Related polytopes
ArmyEpedpy
RegimentEpedpy
DualPentagonal bifrustum
ConjugateElongated pentagrammic bipyramid
Abstract & topological properties
Flag count100
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryH2×A1, order 20
ConvexYes
NatureTame

The elongated pentagonal bipyramid is one of the 92 Johnson solids (J16). It consists of 10 triangles and 5 squares. It can be constructed by inserting a pentagonal prism between the halves of the pentagonal bipyramid.

## Vertex coordinates

An elongated pentagonal bipyramid of edge length 1 has the following vertices:

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