In geometry, the square gyrobicupola is one of the Johnson solids (J29).

The difference is that in this solid, the two halves are rotated 45 degrees with respect to one another.

They were named by Norman Johnson, who first listed these polyhedra in 1966.

This polyhedron is created when an octagonal prism is inserted between the two halves of the square gyrobicupola.

The following formulae for volume and surface area can be used if all faces are regular, with edge length a:[2] The square gyrobicupola forms space-filling honeycombs with tetrahedra, cubes and cuboctahedra; and with tetrahedra, square pyramids, and elongated square bipyramids.