Elongated pentagonal orthocupolarotunda

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Elongated pentagonal orthocupolarotunda
Elongated pentagonal orthocupolarotunda.png
Type Johnson
J39 - J40 - J41
Faces 3x5 triangles
3x5 squares
2+5 pentagons
Edges 70
Vertices 35
Vertex configuration 10(3.43)
Symmetry group C5v
Dual polyhedron -
Properties convex
Johnson solid 40 net.png

In geometry, the elongated pentagonal orthocupolarotunda is one of the Johnson solids (J40). As the name suggests, it can be constructed by elongating a pentagonal orthocupolarotunda (J32) by inserting a decagonal prism between its halves. Rotating either the cupola or the rotunda through 36 degrees before inserting the prism yields an elongated pentagonal gyrocupolarotunda (J41).

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.[1]


The following formulae for volume and surface area can be used if all faces are regular, with edge length a:[2]


  1. ^ Johnson, Norman W. (1966), "Convex polyhedra with regular faces", Canadian Journal of Mathematics, 18: 169–200, doi:10.4153/cjm-1966-021-8, MR 0185507, Zbl 0132.14603 .
  2. ^ Stephen Wolfram, "Elongated pentagonal orthocupolarotunda" from Wolfram Alpha. Retrieved July 25, 2010.

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