What does hexahedron mean?
A hexahedron is a three-dimensional solid bounded by six flat faces. The best-known example is the cube, which is a regular hexahedron because all six of its faces are congruent squares. More broadly, the term includes irregular solids with six faces, such as certain distorted cubes and the block-like forms commonly encountered in architecture and engineering. It is also frequently used in computational geometry, where a three-dimensional cell with six quadrilateral faces is called a hexahedral element. The word belongs to formal mathematical and technical vocabulary rather than everyday speech. Its name reflects its structure: the prefix derives from the Greek word for six, while the ending is used in naming polyhedra. Although “hexahedron” sounds related to “hexagon,” the two terms refer to different geometric forms: one is a solid and the other is a plane figure.
nounA three-dimensional solid with six faces. In geometry, the term may refer to any such polyhedron, although it is especially associated with the regular hexahedron, or cube.
- A polyhedron with six flat faces, especially a cube or another solid used in geometric, architectural, or engineering contexts.
"The architect designed a glass pavilion as an irregular hexahedron."
"The regular hexahedron has six congruent square faces."
"Engineers refined the boundary of the hexahedron before generating the finite-element mesh."
Hexahedra is the standard mathematical plural; hexahedrons is also encountered in less specialized usage.
"The two hexahedra share a common set of boundary conditions."
A cube is the Platonic hexahedron: six square faces, eight vertices, and twelve edges.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does hexahedron come from?
The word combines the Greek combining form hexa-, meaning “six,” with -hedron, a form based on Greek terms for a base or seat and used in the names of polyhedra. The corresponding Greek formation referred to a six-faced solid. The English mathematical term developed through this combination of Greek roots and follows the naming pattern of related forms such as tetrahedron and octahedron.
Related word forms
How hexahedron is actually used
This is primarily a formal mathematical and technical term. In general use, it is often replaced by “cube” when the intended solid is regular.
Easily confused with hexahedron
A hexahedron is a three-dimensional solid with six faces, whereas a hexagon is a two-dimensional polygon with six sides and three dimensions.