Gyroelongated pentagonal cupola

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Gyroelongated pentagonal cupola
Gyroelongated pentagonal cupola.png
Type Johnson
J23 - J24 - J25
Faces 3x5+10 triangles
5 squares
1 pentagon
1 decagon
Edges 55
Vertices 25
Vertex configuration 5(3.4.5.4)
2.5(33.10)
10(34.4)
Symmetry group C5v
Dual polyhedron -
Properties convex
Net
Johnson solid 24 net.png

In geometry, the gyroelongated pentagonal cupola is one of the Johnson solids (J24). As the name suggests, it can be constructed by gyroelongating a pentagonal cupola (J5) by attaching a decagonal antiprism to its base. It can also be seen as a gyroelongated pentagonal bicupola (J46) with one pentagonal cupola removed.

Contents

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]

Area and Volume

With edge length a, the surface area is

and the volume is

Dual polyhedron

The dual of the gyroelongated pentagonal cupola has 25 faces: 10 kites, 5 rhombi, and 10 pentagons.

Dual gyroelongated pentagonal cupolaNet of dual
Dual gyroelongated pentagonal cupola.png Dual gyroelongated pentagonal cupola 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 .

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