gyroelongated pentagonal bicupola

{{Short description|46th Johnson solid}}

{{Infobox polyhedron

|image=gyroelongated_pentagonal_bicupola.png

|type=Johnson
{{math|gyroelongated square bicupola – J{{sub|46}} – gyroelongated pentagonal cupolarotunda}}

|faces=3.10 triangles
10 squares
2 pentagons

|edges=70

|vertices=30

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

|vertex_config={{math|10(3.4.5.4)
2.10(3{{sup|4}}.4)}}

|dual=-

|properties=convex, chiral

|net=Johnson solid 46 net.png

}}

In geometry, the gyroelongated pentagonal bicupola is one of the Johnson solids ({{math|J{{sub|46}}}}). As the name suggests, it can be constructed by gyroelongating a pentagonal bicupola ({{math|pentagonal orthobicupola}} or {{math|pentagonal gyrobicupola}}) by inserting a decagonal antiprism between its congruent halves.

The gyroelongated pentagonal bicupola 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 square 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 right. In the figure of opposite chirality (the mirror image of the illustrated figure), each bottom square would be connected to a square face above it and to the left. The two chiral forms of {{math|J{{sub|46}}}} are not considered different Johnson solids.

{{Johnson solid}}