pseudooctahedra

In geometry, a pseudooctahedron is a polyhedron that is topologically the same as the regular octahedron: it has six vertices, twelve edges, and eight faces, and its edge graph is the octahedral graph. Unlike the regular octahedron, the eight faces of a pseudooctahedron need not be congruent equilateral triangles; they may be polygons of various shapes. Thus a pseudooctahedron is any polyhedron realizable with the octahedral combinatorial type but with nonregular faces.

Such figures can be convex or non-convex and arise as nonregular realizations of the octahedral type. Their exact geometry depends on how the eight faces are arranged around the six vertices, and the symmetry can range from full octahedral symmetry to lower symmetry depending on the face pattern.

In coordination chemistry, the term pseudooctahedral (or pseudooctahedron) describes a six-coordinate metal center whose ligands arrange approximately octahedrally but are distorted; examples include certain octahedral complexes with bulky ligands. The term emphasizes the close, but imperfect, Oh symmetry.

In the literature, the term pseudooctahedron is relatively uncommon and tends to be used informally. Some authors prefer to describe such figures as octahedrally combinatorial realizations or as nonregular octahedra. See also octahedron, disphenoid, and polyhedral types with octahedral graph.