Gyroelongated pentagonal pyramid | |
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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 | |
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 is composed of regular polygon faces but are not uniform polyhedra (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).
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 |
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In geometry, a regular icosahedron is a convex polyhedron with 20 faces, 30 edges and 12 vertices. It is one of the five Platonic solids, and the one with the most faces.
In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that each face must be the same polygon, or that the same polygons join around each vertex. An example of a Johnson solid is the square-based pyramid with equilateral sides ; it has 1 square face and 4 triangular faces. Some authors require that the solid not be uniform before they refer to it as a “Johnson solid”.
In geometry, the gyroelongated square bipyramid, heccaidecadeltahedron, or tetrakis square antiprism is one of the Johnson solids. As the name suggests, it can be constructed by gyroelongating an octahedron by inserting a square antiprism between its congruent halves. It is one of the eight strictly-convex deltahedra.
In geometry, the gyroelongated square pyramid is one of the Johnson solids. 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.
In geometry, the tridiminished icosahedron is one of the Johnson solids (J63).
In geometry, the metabidiminished icosahedron is one of the Johnson solids (J62).
In geometry, the gyroelongated square cupola is one of the Johnson solids (J23). As the name suggests, it can be constructed by gyroelongating a square cupola (J4) by attaching an octagonal antiprism to its base. It can also be seen as a gyroelongated square bicupola (J45) with one square bicupola removed.
In geometry, the gyroelongated pentagonal rotunda is one of the Johnson solids (J25). As the name suggests, it can be constructed by gyroelongating a pentagonal rotunda (J6) by attaching a decagonal antiprism to its base. It can also be seen as a gyroelongated pentagonal birotunda (J48) with one pentagonal rotunda removed.
In geometry, the gyroelongated pentagonal birotunda is one of the Johnson solids (J48). As the name suggests, it can be constructed by gyroelongating a pentagonal birotunda by inserting a decagonal antiprism between its two halves.
In geometry, the gyroelongated square bicupola is one of the Johnson solids (J45). As the name suggests, it can be constructed by gyroelongating a square bicupola by inserting an octagonal antiprism between its congruent halves.
In geometry, the snub square antiprism is one of the Johnson solids . A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform polyhedra. They were named by Norman Johnson, who first listed these polyhedra in 1966.
In geometry, the elongated pentagonal bipyramid or pentakis pentagonal prism is one of the Johnson solids. As the name suggests, it can be constructed by elongating a pentagonal bipyramid by inserting a pentagonal prism between its congruent halves.
In geometry, the gyroelongated pentagonal cupola is one of the Johnson solids (J24). As the name suggests, it can be constructed by gyroelongating a pentagonal cupola (J5) by attaching a decagonal antiprism to its base. It can also be seen as a gyroelongated pentagonal bicupola (J46) with one pentagonal cupola removed.
In geometry, the augmented pentagonal prism is one of the Johnson solids (J52). As the name suggests, it can be constructed by augmenting a pentagonal prism by attaching a square pyramid (J1) to one of its equatorial faces.
In geometry, the biaugmented pentagonal prism is one of the Johnson solids (J53). As the name suggests, it can be constructed by doubly augmenting a pentagonal prism by attaching square pyramids (J1) to two of its nonadjacent equatorial faces.
In geometry, the gyroelongated pentagonal bicupola is one of the Johnson solids (J46). As the name suggests, it can be constructed by gyroelongating a pentagonal bicupola by inserting a decagonal antiprism between its congruent halves.
In geometry, the gyroelongated triangular cupola is one of the Johnson solids (J22). It can be constructed by attaching a hexagonal antiprism to the base of a triangular cupola (J3). This is called "gyroelongation", which means that an antiprism is joined to the base of a solid, or between the bases of more than one solid.
In geometry, the gyroelongated triangular bicupola is one of the Johnson solids (J44). As the name suggests, it can be constructed by gyroelongating a triangular bicupola by inserting a hexagonal antiprism between its congruent halves.
In geometry, the gyroelongated pentagonal cupolarotunda is one of the Johnson solids (J47). As the name suggests, it can be constructed by gyroelongating a pentagonal cupolarotunda by inserting a decagonal antiprism between its two halves.
In geometry, the gyroelongated pyramids are an infinite set of polyhedra, constructed by adjoining an n-gonal pyramid to an n-gonal antiprism.