What does dihedron mean?
A dihedron is a geometric figure made up of exactly two plane faces meeting along an edge. In elementary terms it corresponds to the familiar idea of an angle between two planes — think of an open book, whose two pages form a dihedron about the spine. The term appears chiefly in mathematics, particularly in geometry and crystallography, where describing the precise inclination of one face relative to another matters. In the formal theory of polyhedra, the dihedron occupies a curious position: it is often counted as a degenerate polyhedron, since its two flat faces bound no volume whatsoever. The word derives from Greek roots meaning "two" and "seat" or "face," the same elements found in "polyhedron." While rarely heard outside technical discussion, the dihedron is a useful concept for anyone studying three-dimensional shapes, crystalline structures, or the mathematics of angles in space.
nounA geometric figure formed by two intersecting plane faces or half-planes; in geometry, essentially a solid angle bounded by two planes, also known as an angle between two planes.
- A figure bounded by two intersecting planes; the angle between them.
- (In polyhedron theory) a degenerate 'polyhedron' consisting of only two polygonal faces joined along their edges.
"The crystallographer measured the dihedron formed where the two faces of the mineral met."
"Fold the sheet along the crease and you have a physical model of a dihedron."
"Mathematicians classify the dihedron as a degenerate polyhedron because its two faces enclose no volume."
Both plurals are accepted; "dihedra" follows the classical Greek pattern favored in mathematical writing, while "dihedrons" is the natural English plural.
"The software renders all dihedra formed between successive faces of the mesh."
In strict Euclidean geometry a dihedron is barely a solid at all — it's just two flat faces meeting at an edge, making it one of the degenerate cases that keeps geometers honest.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of dihedron
The word "dihedron" comes from Greek roots: "di-" meaning "twice" or "two," and "hedra" meaning "seat" or, by extension in geometry, "face." It entered English scientific vocabulary during the development of modern geometry, alongside related coinages such as "polyhedron" and "tetrahedron." Cognates sharing the "hedra" root include "cathedral," which descends from the Greek-derived Latin "cathedra," meaning a seat or chair. Its adjective form, "dihedral," is somewhat more common, notably in aviation, where wing dihedral refers to the upward angle of the wings.
How dihedron is actually used
A technical term used mainly in mathematics, especially geometry and crystallography. In everyday contexts it is rare; speakers usually say "angle between two planes" instead.
Easily confused with dihedron
"Dihedral" is primarily an adjective (or a noun for the upward angle of an aircraft's wings) meaning relating to or having two plane surfaces, whereas "dihedron" is the noun naming the figure itself.