| Gyroelongated pentagonal cupolarotunda | |
|---|---|
 | |
| Type | Johnson J46 – J47 – J48 |
| Faces | 7×5 triangles 5 squares 2+5 pentagons |
| Edges | 80 |
| Vertices | 35 |
| Vertex configuration | 5(3.4.5.4) 2.5(3.5.3.5) 2.5(34.4) 2.5(34.5) |
| Symmetry group | C5 |
| Dual polyhedron | - |
| Properties | convex, chiral |
| Net | |
 | |
In geometry, the gyroelongated pentagonal cupolarotunda is one of the Johnson solids (J47). As the name suggests, it can be constructed by gyroelongating a pentagonal cupolarotunda ( J32 or J33 ) by inserting a decagonal antiprism between its two halves.
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A Johnson solid is one of 92 strictly convex polyhedra that are 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 gyroelongated pentagonal cupolarotunda 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 pentagonal 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 left. In the figure of opposite chirality (the mirror image of the illustrated figure), each bottom pentagon would be connected to a square face above it and to the right. The two chiral forms of J47 are not considered different Johnson solids.
