Octangula

Octangula is a historical geometric term most closely associated with a classic stellation of the octahedron known as the Stella Octangula. The phrase Stella Octangula, Latin for "eight-pointed star," describes a compound of two regular tetrahedra that interpenetrate to form a symmetrical eight-pointed star polyhedron. In this arrangement the union of the two tetrahedra yields eight triangular faces, while their intersection is a regular octahedron. The eight vertices lie at the corners of a cube, partitioned into the two tetrahedra’s four-vertex sets.

Geometrically, the Stella Octangula is a regular compound with octahedral symmetry. Each tetrahedron is regular, and together they produce a star-shaped figure that is non-convex but highly symmetric. The central region formed by the overlap is a regular octahedron, and the outer surface comprises the eight triangular faces of the two tetrahedra. The construction is a classical example in polyhedral geometry illustrating how simple regular solids can interpenetrate to create a compound with higher symmetry.

Historically, the Stella Octangula was described by Johannes Kepler in Harmonices Mundi (1619). In older or shorthand usage, the term octangula has occasionally been used to refer to this stellated octahedral compound, though modern literature more often uses the name Stella Octangula to denote the complete figure.

See also: tetrahedron, octahedron, Stella Octangula, polyhedral compounds.