Gyroelongated pentagonal pyramid

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
Gyroelongated pentagonal pyramid
Blue gyroelongated pentagonal pyramid.svg
Type Johnson
J10 - J11 - J12
Faces 3x5 triangles
1 pentagon
Edges 25
Vertices 11
Vertex configuration 5(33.5)
1+5(35)
Symmetry group C5v, [5], (*55)
Rotation group C5, [5]+, (55)
Dual polyhedron -
Properties convex
Net
Gyroelongated pentagonal pyramid net.png

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[edit]

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
Dual gyroelongated pentagonal pyramid.png Dual gyroelongated pentagonal pyramid 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 .