Gyroelongated square cupola

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Gyroelongated square cupola
Gyroelongated square cupola.png
Type Johnson
J22 - J23 - J24
Faces 3x4+8 triangles
1+4 squares
1 octagon
Edges 44
Vertices 20
Vertex configuration 4(3.43)
2.4(33.8)
8(34.4)
Symmetry group C4v
Dual polyhedron -
Properties convex
Net
Johnson solid 23 net.png
An unfolded gyroelongated square cupola
An unfolded gyroelongated square cupola, faces colored by symmetry

In geometry, the gyroelongated square cupola is one of the Johnson solids (J23). As the name suggests, it can be constructed by gyroelongating a square cupola (J4) by attaching an octagonal antiprism to its base. It can also be seen as a gyroelongated square bicupola (J45) with one square bicupola 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 square cupola has 25 faces: 8 kites, 4 rhombi, and 8 quadrilaterals.

Dual gyroelongated square cupola Net of dual
Dual gyroelongated square cupola.png Dual gyroelongated square 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 .