Pentagonal rotunda

Pentagonal rotunda
Type Johnson
J5 - J6 - J7
Faces 10 triangles
1+5 pentagons
1 decagon
Edges 35
Vertices 20
Vertex configuration 2.5(3.5.3.5)
10(3.5.10)
Symmetry group C5v
Dual polyhedron -
Properties convex
Net

In geometry, the pentagonal rotunda is one of the Johnson solids (J6). It can be seen as half an icosidodecahedron.

The 92 Johnson solids were named and described by Norman Johnson in 1966.

Contents

Formulae

The following formulae for volume, surface area, and circumradius can be used if all faces are regular, with edge length a:[1]

V=(\frac{1}{12}(45%2B17\sqrt{5}))a^3\approx6.91776...a^3

A=(\frac{1}{2}\sqrt{5(145%2B58\sqrt{5}%2B2\sqrt{30(65%2B29\sqrt{5})})})a^2\approx22.3472...a^2

C=(\frac{1}{2}(1%2B\sqrt{5}))a\approx1.61803...a

Dual polyhedron

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

Dual pentagonal rotunda Net of dual

Reference

  1. ^ Stephen Wolfram, "Pentagonal Rotunda" from Wolfram Alpha. Retrieved July 21, 2010.

External links