Elongated pentagonal orthobicupola
| Elongated pentagonal orthobicupola | |
|---|---|
 | |
| Type |
Johnson J37 - J38 - J39 |
| Faces |
10 triangles 2.5+10 squares 2 pentagons |
| Edges | 60 |
| Vertices | 30 |
| Vertex configuration |
20(3.43) 10(3.4.5.4) |
| Symmetry group | D5h |
| Dual polyhedron | - |
| Properties | convex |
| Net | |
 | |
In geometry, the elongated pentagonal orthobicupola is one of the Johnson solids (J38).[1] As the name suggests, it can be constructed by elongating a pentagonal orthobicupola (J30) by inserting a decagonal prism between its two congruent halves. Rotating one of the cupolae through 36 degrees before inserting the prism yields an elongated pentagonal gyrobicupola (J39).
A Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform (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.[2]
Formulae
The following formulae for volume and surface area can be used if all faces are regular, with edge length a:[3]
References
- ↑ http://mathworld.wolfram.com/ElongatedPentagonalOrthobicupola.html
- ↑ 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, "Elongated pentagonal orthobicupola" from Wolfram Alpha. Retrieved July 25, 2010.
External links
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