Gyroelongated square pyramid

Summary

In geometry, the gyroelongated square pyramid is one of the Johnson solids (J10). As its name suggests, it can be constructed by taking a square pyramid and "gyroelongating" it, which in this case involves joining a square antiprism to its base.

Gyroelongated square pyramid
Gyroelongated square pyramid.png
TypeJohnson
J9 - J10 - J11
Faces12 triangles
1 square
Edges20
Vertices9
Vertex configuration1(34)
4(33.4)
4(35)
Symmetry groupC4v, [4], (*44)
Rotation groupC4, [4]+, (44)
Dual polyhedron-
Propertiesconvex
Net
Johnson solid 10 net.png

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]

ApplicationsEdit

The Gyroelongated square pyramid represents the capped square antiprismatic molecular geometry:

 

Dual polyhedronEdit

The dual of the gyroelongated square pyramid has 9 faces: 4 kites, 1 square and 4 pentagonal.

Dual gyroelongated square pyramid Net of dual
   

See alsoEdit

External linksEdit


  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.