# Elongated pentagonal bipyramid

Elongated pentagonal bipyramid Rank3
TypeCRF
SpaceSpherical
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$\frac{5+\sqrt5+3\sqrt{25+10\sqrt5}}{12} ≈ 2.32348$ Dihedral angles3–3: $\arccos\left(-\frac{\sqrt5}{3}\right) ≈ 138.18969°$ 3–4: $\arccos\left(-\sqrt{\frac{10-2\sqrt5}{15}}\right) ≈ 127.37737°$ 4–4: 108°
Central density1
Related polytopes
ArmyEpedpy
RegimentEpedpy
DualPentagonal bifrustum
ConjugateElongated pentagrammic bipyramid
Abstract properties
Euler characteristic2
Topological properties
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryH2×A1, order 20
ConvexYes
NatureTame
Discovered by{{{discoverer}}}

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:

• $\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac12\right),$ • $\left(±\frac{1+\sqrt5}{4},\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac12\right),$ • $\left(0,\,±\sqrt{\frac{5+\sqrt5}{10}},\,±\frac12\right),$ • $\left(0,\,0,\,±\frac{1+2\sqrt{\frac{5-\sqrt5}{10}}}{2}\right).$ 