Gyroelongated pentagonal cupolarotunda

{{Short description|47th Johnson solid}}

{{Infobox polyhedron

|image=gyroelongated_pentagonal_cupolarotunda.png

|type=Johnson
{{math|gyroelongated pentagonal bicupola – J{{sub|47}} – gyroelongated pentagonal birotunda}}

|faces=7x5 triangles
5 squares
2+5 pentagons

|edges=80

|vertices=35

|symmetry={{math|C{{sub|5}}}}

|vertex_config={{math|5(3.4.5.4)
2.5(3.5.3.5)
2.5(3{{sup|4}}.4)
2.5(3{{sup|4}}.5)}}

|dual=-

|properties=convex, chiral

|net=Johnson solid 47 net.png

}}

In geometry, the gyroelongated pentagonal cupolarotunda is one of the Johnson solids ({{math|J{{sub|47}}}}). As the name suggests, it can be constructed by gyroelongating a pentagonal cupolarotunda ({{math|pentagonal orthocupolarotunda}} or {{math|pentagonal gyrocupolarotunda}}) by inserting a decagonal antiprism between its two halves.

{{Johnson solid}}

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 {{math|J{{sub|47}}}} are not considered different Johnson solids.