In geometry, the elongated square bipyramid (or elongated octahedron) is the polyhedron constructed by attaching two equilateral square pyramids onto a cube's faces that are opposite each other.

[1][2] A zircon crystal is an example of an elongated square bipyramid.

The elongated square bipyramid is constructed by attaching two equilateral square pyramids onto the faces of a cube that are opposite each other, a process known as elongation.

This construction involves the removal of those two squares and replacing them with those pyramids, resulting in eight equilateral triangles and four squares as their faces.[3].

A convex polyhedron in which all of its faces are regular is a Johnson solid, and the elongated square bipyramid is one of them, denoted as

is the edge length of an elongated square bipyramid.

The height of an elongated square pyramid can be calculated by adding the height of two equilateral square pyramids and a cube.

Its volume is obtained by slicing it into two equilateral square pyramids and a cube, and then adding them:[6]

Its dihedral angle can be obtained in a similar way as the elongated square pyramid, by adding the angle of square pyramids and a cube:[7] The elongated square bipyramid has the dihedral symmetry, the dihedral group

of order eight: it has an axis of symmetry passing through the apices of square pyramids and the center of a cube, and its appearance is symmetrical by reflecting across a horizontal plane.

A special kind of elongated square bipyramid without all regular faces allows a self-tessellation of Euclidean space.

The triangles of this elongated square bipyramid are not regular; they have edges in the ratio 2:√3:√3.

It can be considered a transitional phase between the cubic and rhombic dodecahedral honeycombs.

[1] Here, the cells are colored white, red, and blue based on their orientation in space.

Cross-sections of the honeycomb, through cell centers, produce a chamfered square tiling, with flattened horizontal and vertical hexagons, and squares on the perpendicular polyhedra.

With regular faces, the elongated square bipyramid can form a tessellation of space with tetrahedra and octahedra.