Elongated pentagonal bipyramid

Elongated pentagonal bipyramid
(3D model) (OFF file)
Rank	3
Type	CRF
Space	Spherical
Notation
Bowers style acronym	Epedpy
Coxeter diagram	oxxo5oooo&#xt
Elements
Faces	10 triangles, 5 squares
Edges	5+10+10
Vertices	2+10
Vertex figures	2 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 angles	3–3: $\arccos\left(-\frac{\sqrt5}{3}\right) ≈ 138.18969°$
	3–4: $\arccos\left(-\sqrt{\frac{10-2\sqrt5}{15}}\right) ≈ 127.37737°$
	4–4: 108°
Central density	1
Related polytopes
Army	Epedpy
Regiment	Epedpy
Dual	Pentagonal bifrustum
Conjugate	Elongated pentagrammic bipyramid
Abstract properties
Euler characteristic	2
Topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	H2×A1, order 20
Convex	Yes
Nature	Tame
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:

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

External links

• Klitzing, Richard. "epedpy".

• Quickfur. "The Elongated Pentagonal Bipyramid".

• Wikipedia Contributors. "Elongated pentagonal bipyramid".
• McCooey, David. "Elongated Pentagonal Dipyramid J16"