Gyroelongated pentagonal cupolarotunda
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| 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 | - |
| Properties | convex, chiral |
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.
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.
The 92 Johnson solids were named and described by Norman Johnson in 1966.
