Gyroelongated pentagonal pyramid
Encyclopedia
In geometry
, the gyroelongated pentagonal pyramid is one of the Johnson solid
s (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.
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).
The 92 Johnson solids were named and described by Norman Johnson in 1966.
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, the gyroelongated pentagonal pyramid is one of the Johnson solid
Johnson solid
In geometry, a Johnson solid is a strictly convex polyhedron, each face of which is a regular polygon, but which is not uniform, i.e., not a Platonic solid, Archimedean solid, prism or antiprism. There is no requirement that each face must be the same polygon, or that the same polygons join around...
s (J11). As its name suggests, it is formed by taking a pentagonal pyramid
Pentagonal pyramid
In geometry, a pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point . Like any pyramid, it is self-dual....
and "gyroelongating" it, which in this case involves joining a pentagonal antiprism
Antiprism
In geometry, an n-sided antiprism is a polyhedron composed of two parallel copies of some particular n-sided polygon, connected by an alternating band of triangles...
to its base.
It can also be seen as a diminished icosahedron, an icosahedron
Icosahedron
In geometry, an icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of the five Platonic solids....
with the top (a pentagonal pyramid
Pentagonal pyramid
In geometry, a pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point . Like any pyramid, it is self-dual....
, J2) chopped off by a plane. Other Johnson solids can be formed by cutting off multiple pentagonal pyramids from an icosahedron: the pentagonal antiprism
Pentagonal antiprism
In geometry, the pentagonal antiprism is the third in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps. It consists of two pentagons joined to each other by a ring of 10 triangles for a total of 12 faces...
and metabidiminished icosahedron
Metabidiminished icosahedron
In geometry, the metabidiminished icosahedron is one of the Johnson solids . The name refers to one way of constructing it, by removing two pentagonal pyramids from a regular icosahedron, replacing two sets of five triangular faces of the icosahedron with two adjacent pentagonal faces...
(two pyramids removed), and the tridiminished icosahedron
Tridiminished icosahedron
In geometry, the tridiminished icosahedron is one of the Johnson solids .The 92 Johnson solids were named and described by Norman Johnson in 1966.- Related polytopes :...
(three pyramids removed).
The 92 Johnson solids were named and described by Norman Johnson in 1966.
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 |
|---|---|