Space-filling polyhedra

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

three-sided prism

thumb|3D model of a gyrobifastigium

prism with hexagonal base

tiling of 3-or-more dimensional Euclidean or hyperbolic space

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.

polyhedron formed by six congruent rhombi

polyhedron

thumb|upright=1.2|Five types of parallelohedron. Top: cube, [[hexagonal prism, rhombic dodecahedron. Bottom: elongated dodecahedron, truncated octahedron. The colors partition the edges into zones; for each zone, the faces containing edges of that color form a belt. Choosing one edge of each color produces a system of generators for each polyhedron.]] In geometry, a parallelohedron or Fedorov polyhedron is a convex polyhedron that can be translated without rotations to fill Euclidean space, producing a honeycomb in which all copies of the polyhedron meet face-to-face. Evgraf Fedorov identified

self I intersecting polyhedron with 12 faces