In
geometry, the gyroelongated pentagonal pyramid is one of the
Johnson solid
In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that isohedral, each face must be the same polygon, or that the same polygons join around each Vertex (geometry), ver ...
s (). 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.
It can also be seen as a diminished icosahedron, an
icosahedron
In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons".
There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrica ...
with the top (a
pentagonal pyramid, ) 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.
External links
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Johnson solids
Pyramids and bipyramids
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