Definition

Noun: A regular octahedron is a specific three-dimensional geometric shape. It is a type of octahedron where all eight faces are congruent equilateral triangles. It is one of the five Platonic solids, meaning it is a convex polyhedron with identical regular polygonal faces meeting at identical angles.

Usage

The term is used in geometry, mathematics, crystallography, and related fields to describe this precise polyhedron. * In geometry class, we constructed a model of a regular octahedron. * The diamond crystal often forms in the shape of a regular octahedron.

Advanced Usage

• As a Platonic Solid: The regular octahedron is dual to the cube. This means the center of each face of a cube corresponds to a vertex of a regular octahedron, and vice versa.
• In Symmetry: It possesses high symmetry, specifically octahedral symmetry.

Variants and Related Words

• Octahedron (noun): Any polyhedron with eight faces. A regular octahedron is a specific, highly symmetric case.
• Platonic solid (noun): Any of the five convex regular polyhedra (tetrahedron, cube, octahedron, dodecahedron, icosahedron).

Synonyms

• Platonic octahedron

Related Phrases / Concepts

• Dual polyhedron: The cube is the dual polyhedron of the regular octahedron.
• Equilateral triangle: The shape of each identical face of a regular octahedron.

Noun

1. an octahedron with eight equilateral triangles as faces