Elongated pentagonal pyramid
Elongated pentagonal pyramid | |
---|---|
Type | Johnson J8 – J9 – J10 |
Faces | 5 triangles 5 squares 1 pentagon |
Edges | 20 |
Vertices | 11 |
Vertex configuration | 5(42.5) 5(32.42) 1(35) |
Symmetry group | C5v, [5], (*55) |
Rotation group | C5, [5]+, (55) |
Dual polyhedron | self |
Properties | convex |
Net | |
In geometry, the elongated pentagonal pyramid is one of the Johnson solids (J9). As the name suggests, it can be constructed by elongating a pentagonal pyramid (J2) by attaching a pentagonal prism 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]
Formulae
The following formulae for the height (), surface area () and volume () can be used if all faces are regular, with edge length :[2]
Dual polyhedron
The dual of the elongated pentagonal pyramid has 11 faces: 5 triangular, 1 pentagonal and 5 trapezoidal. It is topologically identical to the Johnson solid.
Dual elongated pentagonal pyramid | Net of dual |
---|---|
See also
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.
- ^ Sapiña, R. "Area and volume of the Johnson solid J9". Problemas y ecuaciones (in Spanish). ISSN 2659-9899. Retrieved 2020-08-30.
External links
- Weisstein, Eric W., "Johnson solid" ("Elongated pentagonal pyramid") at MathWorld.
- v
- 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
This polyhedron-related article is a stub. You can help Wikipedia by expanding it. |
- v
- t
- e