Pentagonal gyrobicupola
Pentagonal gyrobicupola | |
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Type | Bicupola, Johnson J30 – J31 – J32 |
Faces | 10 triangles 10 squares 2 pentagons |
Edges | 40 |
Vertices | 20 |
Vertex configuration | 10(3.4.3.4) 10(3.4.5.4) |
Symmetry group | D5d |
Dual polyhedron | Elongated pentagonal trapezohedron |
Properties | convex |
Net | |
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In geometry, the pentagonal gyrobicupola is one of the Johnson solids (J31). Like the pentagonal orthobicupola (J30), it can be obtained by joining two pentagonal cupolae (J5) along their bases. The difference is that in this solid, the two halves are rotated 36 degrees with respect to one another.
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]
The pentagonal gyrobicupola is the third in an infinite set of gyrobicupolae.
The pentagonal gyrobicupola is what you get when you take a rhombicosidodecahedron, chop out the middle parabidiminished rhombicosidodecahedron (J80), and paste the two opposing cupolae back together.
Formulae
The following formulae for volume and surface area can be used if all faces are regular, with edge length a:[2]
References
- ^ 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.
- ^ Stephen Wolfram, "Pentagonal gyrobicupola" from Wolfram Alpha. Retrieved July 24, 2010.
External links
- Weisstein, Eric W., "Pentagonal gyrobicupola" ("Johnson solid") at MathWorld.
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- 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
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