Zonohedra

A cube is a three-dimensional solid object in geometry. A cube has eight vertices and twelve straight edges of the same length, so that these edges form six square faces of the same size. It is an example of a polyhedron.

{| class=wikitable align="right" !bgcolor=#e7dcc3 colspan=2|Parallelepiped |- |align=center colspan=2|240px|Parallelepiped |- |bgcolor=#e7dcc3|Type||PrismPlesiohedron |- |bgcolor=#e7dcc3|Faces||6 parallelograms |- |bgcolor=#e7dcc3|Edges||12 |- |bgcolor=#e7dcc3|Vertices||8 |- |bgcolor=#e7dcc3|Symmetry group||Ci, [2+,2+], (×), order 2 |- |bgcolor=#e7dcc3|Properties||convex, zonohedron |}

{| class="wikitable" align="right" style="margin-left:10px" width="250" !bgcolor=#e7dcc3 colspan=2|Rhombohedron |- |align=center colspan=2|240px|Rhombohedron |- |bgcolor=#e7dcc3|Type||prism |- |bgcolor=#e7dcc3|Faces||6 rhombi |- |bgcolor=#e7dcc3|Edges||12 |- |bgcolor=#e7dcc3|Vertices||8 |- |bgcolor=#e7dcc3|Symmetry group||Ci , [2+,2+], (×), order 2 |- |bgcolor=#e7dcc3|Properties||convex, equilateral, zonohedron, parallelohedron |}

Catalan polyhedron

Archimedean solid

Catalan polyhedron

Archimedean solid

Archimedean solid

In geometry, a zonohedron is a convex polyhedron that is centrally symmetric, every face of which is a polygon that is centrally symmetric (a zonogon). Any zonohedron may equivalently be described as the Minkowski sum of a set of line segments in three-dimensional space, or as a three-dimensional projection of a hypercube. Zonohedra were originally defined and studied by E. S. Fedorov, a Russian crystallographer. More generally, in any dimension, the Minkowski sum of line segments forms a polytope known as a zonotope.

prism with hexagonal base

polyhedron formed by six congruent rhombi

thumb|Example of a hexahedronIn geometry, a cuboid is a hexahedron with quadrilateral faces, meaning it is a polyhedron with six faces; it has eight vertices and twelve edges. A rectangular cuboid (sometimes also called a "cuboid") has all right angles and equal opposite rectangular faces. Etymologically, "cuboid" means "like a cube", in the sense of a convex solid which can be transformed into a cube (by adjusting the lengths of its edges and the angles between its adjacent faces). A cuboid is a convex polyhedron whose polyhedral graph is the same as that of a cube.

sixth in an infinite set of prisms, formed by square sides and two regular octagon caps

polyhedron

12-sided box

mathematical concept

convex polyhedron with 90 rhombic faces

geometrical shape

3D geometric shape