Bipiramid

Bipiramid, or bipyramid, is a geometric term describing a polyhedron formed by joining two congruent pyramids along their bases. If the shared base is an n-gon, the resulting shape is called an n-bipyramid. In general, a bipyramid has 2n triangular faces, n+2 vertices, and 3n edges. The simplest nondegenerate example is the triangular bipyramid (n = 3), which has six faces, five vertices, and nine edges. Other common cases include the square bipyramid (n = 4) with eight faces, and the pentagonal bipyramid (n = 5) with ten faces.

In chemistry, the term bipyramidal is used to describe certain five-coordinate molecular geometries, notably the trigonal bipyramidal arrangement. In a trigonal bipyramidal molecule, three ligands occupy equatorial positions around a central atom at about 120° to each other, while two ligands occupy axial positions opposite each other at about 180°. This geometry is common for many main-group and transition-metal complexes, especially in gas phase or when ligand sets favor a five-coordinate core. Classic example: phosphorus pentachloride (PCl5) in the gas phase adopts a trigonal bipyramidal structure. Real-world compounds may deviate from ideal angles due to ligand effects and electronic factors. There is also a square pyramidal five-coordinate arrangement observed in some complexes, though it is not a bipyramidal geometry in the strict sense.

Bipyramidal shapes are encountered in various fields, including crystallography, supramolecular chemistry, and mineralogy, whenever two pyramidal units share a common base.