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(
Symmetry group C5v
Dual polyhedron -
Properties convex
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.

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]

Dual polyhedron[edit]

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

Dual gyroelongated pentagonal cupola Net of dual
Dual gyroelongated pentagonal cupola.png Dual gyroelongated pentagonal cupola net.png

External links[edit]

  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 .