Elongated pentagonal bipyramid

Elongated pentagonal bipyramid
(3D model) (OFF file)
Rank	3
Type	CRF
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	${\frac {5+{\sqrt {5}}+3{\sqrt {25+1{\sqrt {5}}}}}{12}}\approx 2.32348$
Dihedral angles	3–3: $\arccos \left(-{\frac {\sqrt {5}}{3}}\right)\approx 138.18969^{\circ }$
	3–4: $\arccos \left(-{\sqrt {\frac {10-2{\sqrt {5}}}{15}}}\right)\approx 127.37737^{\circ }$
	4–4: 108°
Central density	1
Number of external pieces	15
Level of complexity	5
Related polytopes
Army	Epedpy
Regiment	Epedpy
Dual	Pentagonal bifrustum
Conjugate	Elongated pentagrammic bipyramid
Abstract & topological properties
Flag count	100
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	H2×A1, order 20
Convex	Yes
Nature	Tame

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:

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

External links

• Klitzing, Richard. "epedpy".
• Quickfur. "The Elongated Pentagonal Bipyramid".

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