What does polyhedron mean?
A polyhedron is a three-dimensional geometric solid whose outside is formed by flat polygonal faces. These faces meet along edges, and the edges meet at vertices, creating a bounded structure with no curved surfaces. A cube, tetrahedron, octahedron, and dodecahedron are all examples. The word is especially important in geometry, architecture, crystallography, and the design of three-dimensional models and structures. Its name reflects its construction: the Greek prefix poly- means 'many', while -hedron refers to a face or seat, so a polyhedron is fundamentally a many-faced solid. The plural 'polyhedra' is standard in mathematical writing, though 'polyhedrons' is also encountered. The term is distinct from 'polygon', which describes a flat two-dimensional figure rather than a solid.
nounA three-dimensional solid whose surface is made up of flat polygonal faces joined along straight edges. In geometry, a polyhedron has no curved surfaces.
- A three-dimensional solid bounded by flat polygonal faces, joined along edges and meeting at vertices.
"The exhibition displays a remarkable polyhedron made entirely from transparent glass."
"A cube is the simplest example of a polyhedron."
"The mathematician studied the symmetry of regular polyhedra."
The standard mathematical plural is 'polyhedra'. 'Polyhedrons' is also attested but is less customary.
"Several polyhedra were displayed in the mathematics gallery."
A polygon is flat; a polyhedron is what happens when flat faces close around a three-dimensional interior.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of polyhedron
The word comes from Greek polus, meaning 'many', combined with -hedron, from Greek hedra, meaning 'seat' or 'base'. The form polyhedron was adopted into English through Latin and French usage. Its name follows the Greek construction for three-dimensional forms and reflects the idea of a solid composed of many faces.
Related word forms
How polyhedron is actually used
In formal mathematical and technical writing, this is the standard term for a solid made from polygonal faces. The plural is most commonly 'polyhedra'; 'polyhedrons' is also used but is less customary.
Easily confused with polyhedron
A polygon is a two-dimensional plane figure, whereas a polyhedron is a three-dimensional solid bounded by polygonal faces.