Final answer:
A hexahedron is a polyhedron with six faces, and while it is often equated with a cube, the term does not specify the shape of the faces, just the quantity. The term is distinct from octahedron and icosahedron, which have eight and twenty faces respectively.
Step-by-step explanation:
A hexahedron is a prism whose base is commonly recognized as a polygon with six faces. In most cases, when people refer to a hexahedron, they are thinking of a cube, which has square faces. However, the term hexahedron does not necessarily specify the shape of the faces, just the number of them.
In geometry, different types of polyhedra such as the octahedron and icosahedron are studied to understand the properties and symmetry of complex shapes. An octahedron has eight faces, not six, which is a common point of confusion. To distinguish it from an octahedron, remember that a hexahedron has six faces, whereas an octahedron is described by figures like the double square pyramid or as lying on one of its triangular faces when considering its place in a lattice structure. An icosahedron, on the other hand, has 20 faces made up of equilateral triangles.
The description of geometrical shapes and solids such as hexahedron, octahedron, and icosahedron is fundamental in mathematics and is particularly pertinent in the fields of geometry and crystallography.