A hexahedron (plural: hexahedra or hexahedrons) or sexahedron (plural: sexahedra or sexahedrons) is any
polyhedron with six
faces. A
cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross.
The cube is the on ...
, for example, is a
regular
The term regular can mean normal or in accordance with rules. It may refer to:
People
* Moses Regular (born 1971), America football player
Arts, entertainment, and media Music
* "Regular" (Badfinger song)
* Regular tunings of stringed instrum ...
hexahedron with all its faces
square
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length a ...
, and three squares around each
vertex.
There are seven topologically distinct ''convex'' hexahedra,
Counting polyhedra
/ref> one of which exists in two mirror image forms. There are three topologically distinct concave hexahedra. Two polyhedra are "topologically distinct" if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges or the angles between edges or faces.
Convex, Cuboid
Convex, Others
Concave
There are three further topologically distinct hexahedra that can only be realised as ''concave'' figures:
A digonal antiprism can be considered a degenerate form of hexahedron, having two opposing digonal faces and four triangular faces. However, digons are usually disregarded in the definition of non-spherical polyhedra, and this case is often simply considered a tetrahedron and the four remaining triangular faces considered to compose the full solid.
See also
* Prismatoid
References
External links
Polyhedra with 4-7 Faces
by Steven Dutch
{{Polyhedra
6 (number)
Polyhedra