Gyroelongated square pyramid

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Gyroelongated square pyramid
Gyroelongated square pyramid.png
Type Johnson
J9 - J10 - J11
Faces 3*4 triangles
1 square
Edges 20
Vertices 9
Vertex configuration 1(34)
4(33.4)
4(35)
Symmetry group C4v, [4], (*44)
Rotation group C4, [4]+, (44)
Dual polyhedron -
Properties convex
Net
Johnson solid 10 net.png

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.

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]

Applications[edit]

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

Nonahydridorhenate-3D-balls.png

Dual polyhedron[edit]

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

Dual gyroelongated square pyramid Net of dual
Dual gyroelongated square pyramid.png Dual gyroelongated square pyramid net.png

See also[edit]

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 .