Editing Octahedron (section)

===As a square bipyramid===
[[File:Square bipyramid.png|thumb|upright=0.6|Square bipyramid]]
Many octahedra of interest are '''square bipyramids'''.{{r|oh}} A square bipyramid is a [[bipyramid]] constructed by attaching two square pyramids base-to-base. These pyramids cover their square bases, so the resulting polyhedron has eight triangular faces.{{r|trigg}}

A square bipyramid is said to be right if the square pyramids are symmetrically regular and both of their apices are on the line passing through the base's center; otherwise, it is oblique.{{r|polya}} The resulting bipyramid has [[Point groups in three dimensions|three-dimensional point group]] of [[dihedral group]] <math> D_{4\mathrm{h}} </math> of sixteen: the appearance is symmetrical by rotating around the axis of symmetry that passing through apices and base's center vertically, and it has mirror symmetry relative to any bisector of the base; it is also symmetrical by reflecting it across a horizontal plane.{{r|ak}} Therefore, this square bipyramid is [[face-transitive]] or isohedral.{{r|mclean}}

If the edges of a square bipyramid are all equal in length, then that square bipyramid is a regular octahedron.