Elongated pentagonal rotunda

Elongated pentagonal rotunda
Type Johnson
J20 - J21 - J22
Faces 2.5 triangles
2.5 squares
1+5 pentagons
1 decagon
Edges 55
Vertices 30
Vertex configuration 10(42.10)
10(3.42.5)
2.5(3.5.3.5)
Symmetry group C5v
Dual polyhedron -
Properties convex
Net

In geometry, the elongated pentagonal rotunda is one of the Johnson solids (J21). As the name suggests, it can be constructed by elongating a pentagonal rotunda (J6) by attaching a decagonal prism to its base. It can also be seen as an elongated pentagonal orthobirotunda (J42) with one pentagonal rotunda removed.

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

Contents

Formulae

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

V=\frac{1}{12}(45%2B17\sqrt{5}%2B30\sqrt{5%2B2\sqrt{5}})a^3\approx14.612...a^3

A=\frac{1}{2}(20%2B\sqrt{5(145%2B58\sqrt{5}%2B2\sqrt{30(65%2B29\sqrt{5})})})a^2\approx32.3472...a^2

Dual polyhedron

The dual of the elongated pentagonal rotunda has 30 faces: 10 isoceles triangles, 10 rhombi, and 10 quadrilaterals.

Dual elongated pentagonal rotunda Net of dual

References

  1. ^ Stephen Wolfram, "Elongated pentagonal rotunda" from Wolfram Alpha. Retrieved July 22, 2010.

External links