What is "octahedron"

Octahedron \Oc`ta*he"dron\, n. [Gr.?, fr. ? eight-side; 'okta- (for 'oktw` eight) + ? seat, base, from ? to sit.] (Geom.) A solid bounded by eight faces. The regular octahedron is contained by eight equal equilateral triangles.

1560s, from Greek oktahedron, neuter of oktahedros "eight-sided," from okta- "eight" (see octa-) + hedra "seat" (see sedentary). Related: Octahedral.

n. (context geometry English) a polyhedron with eight faces; the regular octahedron has regular triangles as faces and is one of the Platonic solids.

1. n. any polyhedron having eight plane faces

2. [also: octahedra (pl)]

In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex.

A regular octahedron is the dual polyhedron of a cube. It is a rectified tetrahedron. It is a square bipyramid in any of three orthogonal orientations. It is also a triangular antiprism in any of four orientations.

An octahedron is the three-dimensional case of the more general concept of a cross polytope.

A regular octahedron is a 3-ball in the Manhattan metric.

Octahedron is the fifth full-length studio album by American progressive rock band The Mars Volta, released on June 23, 2009. The album was released by Warner Bros. Records in North America and Mercury Records worldwide. It is the last studio album to feature drummer Thomas Pridgen and guitarist John Frusciante, and the first not to feature contributions from keyboardist Isaiah "Ikey" Owens.

Regarding the release, vocalist Cedric Bixler-Zavala states that the band "wanted to make the opposite of all the records we've done. All along we've threatened people that we'd make a pop record, and now we have."

It debuted at number 112 on the Billboard 200 albums chart with sales of 29,980 in its first week of release.