# Elongated pentagonal orthobicupola

Elongated pentagonal orthobicupola
Type Johnson
J37 - J38 - J39
Faces 10 triangles
2x5+10 squares
2 pentagons
Edges 60
Vertices 30
Vertex configuration 20(3.43)
10(3.4.5.4)
Symmetry group D5h
Dual polyhedron -
Properties convex
Net

In geometry, the elongated pentagonal orthobicupola is one of the Johnson solids (J38).[1] As the name suggests, it can be constructed by elongating a pentagonal orthobicupola (J30) by inserting a decagonal prism between its two congruent halves. Rotating one of the cupolae through 36 degrees before inserting the prism yields an elongated pentagonal gyrobicupola (J39).

A Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform (that is, they are not Platonic solids, Archimedean solids, prisms, or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.[2]

## Formulae

The following formulae for volume and surface area can be used if all faces are regular, with edge length a:[3]

${\displaystyle V={\frac {1}{6}}(10+8{\sqrt {5}}+15{\sqrt {5+2{\sqrt {5}}}})a^{3}\approx 12.3423...a^{3}}$

${\displaystyle A=(20+{\sqrt {{\frac {5}{2}}(10+{\sqrt {5}}+{\sqrt {75+30{\sqrt {5}}}})}})a^{2}\approx 27.7711...a^{2}}$