In geometry, the **gyroelongated square bicupola** is one of the Johnson solids (*J*_{45}). As the name suggests, it can be constructed by gyroelongating a square bicupola (*J*_{28} or *J*_{29}) by inserting an octagonal antiprism between its congruent halves.

The gyroelongated square 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 left half of the figure is connected by a path of two triangular faces to a square face below it and to the right. In the figure of opposite chirality (the mirror image of the illustrated figure), each square on the left would be connected to a square face above it and to the right. The two chiral forms of *J*_{45} are not considered different Johnson solids.

The 92 Johnson solids were named and described by Norman Johnson in 1966.

### Famous quotes containing the word square:

“In old times people used to try and *square* the circle; now they try and devise schemes for satisfying the Irish nation.”

—Samuel Butler (1835–1902)