In geometry, the elongated pentagonal gyrocupolarotunda is one of the Johnson solids (J41). As the name suggests, it can be constructed by elongating a pentagonal gyrocupolarotunda (J33) by inserting a decagonal prism between its halves. Rotating either the pentagonal cupola (J5) or the pentagonal rotunda (J6) through 36 degrees before inserting the prism yields an elongated pentagonal orthocupolarotunda (J40).
| Elongated pentagonal gyrocupolarotunda | |
|---|---|
 | |
| Type | Johnson J40 – J41 – J42 |
| Faces | 3x5 triangles 3x5 squares 2+5 pentagons |
| Edges | 70 |
| Vertices | 35 |
| Vertex configuration | 10(3.43) 10(3.42.5) 5(3.4.5.4) 2.5(3.5.3.5) |
| Symmetry group | C5v |
| Dual polyhedron | - |
| Properties | convex |
| Net | |
 | |
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
editThe following formulae for volume and surface area can be used if all faces are regular, with edge length a:[2]
References
edit- ^ 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 gyrocupolarotunda" from Wolfram Alpha. Retrieved July 25, 2010.
External links
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