In geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, the square orthobicupola is one of the Johnson solid

Johnson solid

In geometry, a Johnson solid is a strictly convex polyhedron, each face of which is a regular polygon, but which is not uniform, i.e., not a Platonic solid, Archimedean solid, prism or antiprism. There is no requirement that each face must be the same polygon, or that the same polygons join around...

s (J₂₈). As the name suggests, it can be constructed by joining two square cupola

Square cupola

In geometry, the square cupola, sometimes called lesser dome, is one of the Johnson solids . It can be obtained as a slice of the rhombicuboctahedron...

e (J₄) along their octagonal bases, matching like faces. A 45-degree rotation of one cupola before the joining yields a square gyrobicupola

Square gyrobicupola

In geometry, the square gyrobicupola is one of the Johnson solids . Like the square orthobicupola , it can be obtained by joining two square cupolae along their bases...

 (J₂₉).

The square orthobicupola is the second in an infinite set of orthobicupolae

Bicupola (geometry)

In geometry, a bicupola is a solid formed by connecting two cupolae on their bases.There are two classes of bicupola because each cupola half is bordered by alternating triangles and squares...

.

The square orthobicupola can be elongated by the insertion of an octagonal prism

Octagonal prism

In geometry, the octagonal prism is the sixth in an infinite set of prisms, formed by square sides and two regular octagon caps.If faces are all regular, it is a semiregular polyhedron.- Use :...

 between its two cupolae to yield a rhombicuboctahedron

Rhombicuboctahedron

In geometry, the rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid with eight triangular and eighteen square faces. There are 24 identical vertices, with one triangle and three squares meeting at each. Note that six of the squares only share vertices with the triangles...

, or collapsed by the removal of an irregular hexagonal prism

Hexagonal prism

In geometry, the hexagonal prism is a prism with hexagonal base. The shape has 8 faces, 18 edges, and 12 vertices.Since it has eight faces, it is an octahedron. However, the term octahedron is primarily used to refer to the regular octahedron, which has eight triangular faces...

 to yield an elongated square dipyramid

Elongated square dipyramid

In geometry, the elongated square bipyramid is one of the Johnson solids . As the name suggests, it can be constructed by elongating an octahedron by inserting a cube between its congruent halves....

 (J₁₅), which itself is merely an elongated octahedron

Octahedron

In geometry, an octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex....

.

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