# Gyroelongated pentagonal pyramid

Gyroelongated pentagonal pyramid
TypeJohnson
J10 - J11 - J12
Faces3x5 triangles
1 pentagon
Edges25
Vertices11
Vertex configuration5(33.5)
1+5(35)
Symmetry groupC5v, [5], (*55)
Rotation groupC5, [5]+, (55)
Dual polyhedron-
Propertiesconvex
Net

In geometry, the gyroelongated pentagonal pyramid is one of the Johnson solids (J11). As its name suggests, it is formed by taking a pentagonal pyramid and "gyroelongating" it, which in this case involves joining a pentagonal 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]

It can also be seen as a diminished icosahedron, an icosahedron with the top (a pentagonal pyramid, J2) chopped off by a plane. Other Johnson solids can be formed by cutting off multiple pentagonal pyramids from an icosahedron: the pentagonal antiprism and metabidiminished icosahedron (two pyramids removed), and the tridiminished icosahedron (three pyramids removed).

## Dual polyhedron

The dual of the gyroelongated pentagonal pyramid has 11 faces: 5 kites, 1 regular pentagonal and 5 irregular pentagons.

Dual gyroelongated pentagonal pyramid Net of dual