Gyroelongated pentagonal bicupola
Gyroelongated pentagonal bicupola | |
---|---|
Type | Johnson J45 – J46 – J47 |
Faces | 3.10 triangles 10 squares 2 pentagons |
Edges | 70 |
Vertices | 30 |
Vertex configuration | 10(3.4.5.4) 2.10(34.4) |
Symmetry group | D5 |
Dual polyhedron | - |
Properties | convex, chiral |
Net | |
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 (J30 or J31) by inserting a decagonal antiprism between its congruent halves.
The gyroelongated pentagonal bicupola is one of five Johnson solids which are chiral, meaning that they have a "left-handed" and a "right-handed" form. In the illustration to the right, each square face on the bottom half of the figure is connected by a path of two triangular faces to a square face above it and to the right. In the figure of opposite chirality (the mirror image of the illustrated figure), each bottom square would be connected to a square face above it and to the left. The two chiral forms of J46 are not considered different Johnson solids.
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]
Area and Volume
With edge length a, the surface area is
and the volume is
External links
- Weisstein, Eric W., "Gyroelongated pentagonal bicupola" ("Johnson solid") at MathWorld.
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- t
- e
- elongated triangular pyramid
- elongated square pyramid
- elongated pentagonal pyramid
- gyroelongated square pyramid
- gyroelongated pentagonal pyramid
- triangular bipyramid
- pentagonal bipyramid
- elongated triangular bipyramid
- elongated square bipyramid
- elongated pentagonal bipyramid
- gyroelongated square bipyramid
- elongated triangular cupola
- elongated square cupola
- elongated pentagonal cupola
- elongated pentagonal rotunda
- gyroelongated triangular cupola
- gyroelongated square cupola
- gyroelongated pentagonal cupola
- gyroelongated pentagonal rotunda
- gyrobifastigium
- triangular orthobicupola
- square orthobicupola
- square gyrobicupola
- pentagonal orthobicupola
- pentagonal gyrobicupola
- pentagonal orthocupolarotunda
- pentagonal gyrocupolarotunda
- pentagonal orthobirotunda
- elongated triangular orthobicupola
- elongated triangular gyrobicupola
- elongated square gyrobicupola
- elongated pentagonal orthobicupola
- elongated pentagonal gyrobicupola
- elongated pentagonal orthocupolarotunda
- elongated pentagonal gyrocupolarotunda
- elongated pentagonal orthobirotunda
- elongated pentagonal gyrobirotunda
- gyroelongated triangular bicupola
- gyroelongated square bicupola
- gyroelongated pentagonal bicupola
- gyroelongated pentagonal cupolarotunda
- gyroelongated pentagonal birotunda
- augmented truncated tetrahedron
- augmented truncated cube
- biaugmented truncated cube
- augmented truncated dodecahedron
- parabiaugmented truncated dodecahedron
- metabiaugmented truncated dodecahedron
- triaugmented truncated dodecahedron
- gyrate rhombicosidodecahedron
- parabigyrate rhombicosidodecahedron
- metabigyrate rhombicosidodecahedron
- trigyrate rhombicosidodecahedron
- diminished rhombicosidodecahedron
- paragyrate diminished rhombicosidodecahedron
- metagyrate diminished rhombicosidodecahedron
- bigyrate diminished rhombicosidodecahedron
- parabidiminished rhombicosidodecahedron
- metabidiminished rhombicosidodecahedron
- gyrate bidiminished rhombicosidodecahedron
- tridiminished rhombicosidodecahedron
- ^ 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.