Pentagonal rotunda

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Pentagonal rotunda
Pentagonal rotunda.png
J5 - J6 - J7
Faces10 triangles
1+5 pentagons
1 decagon
Vertex configuration2.5(
Symmetry groupC5v
Rotation groupC5, [5]+, (55)
Dual polyhedron-
Pentagonal Rotunda Net.svg

In geometry, the pentagonal rotunda is one of the Johnson solids (J6). It can be seen as half of an icosidodecahedron, or as half of a pentagonal orthobirotunda. It has a total of 17 faces.

A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform polyhedra (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, surface area, circumradius, and height are valid if all faces are regular, with edge length a:[2]

Dual polyhedron[edit]

The dual of the pentagonal rotunda has 20 faces: 10 triangular, 5 rhombic, and 5 kites.

Dual pentagonal rotunda Net of dual
Dual pentagonal rotunda.png Dual pentagonal rotunda net.png


  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. ^ "Pentagonal rotunda". Wolfram Alpha Site. Retrieved July 21, 2010.

External links[edit]