Edges 80 Symmetry group C5 | Vertices 35 | |
 | ||
Type Johnson
J46 - J47 - J48 Faces 7x5 triangles
5 squares
2+5 pentagons Vertex configuration 5(3.4.5.4)
2.5(3.5.3.5)
2.5(3.4)
2.5(3.5) | ||
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.
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.
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.