Parallelogon

{{Not to be confused with|zonogon|text=zonogon, a polygon with parallel opposite sides, that does not necessarily tile a plane but must be convex}}{{short description|Polygon able to tessellate edge-to-edge, without rotation}}

File:Parallelogons as 2 or 3 vectors.png

File:2d-bravais.svg in two dimensions, related to the parallelogon tessellations by their five symmetry variations.]]

In geometry, a parallelogon is a polygon with parallel opposite sides (hence the name) that can tile a plane by translation (rotation is not permitted).{{Cite journal |last=Grünbaum |first=Branko |date=2010-12-01 |title=The Bilinski Dodecahedron and Assorted Parallelohedra, Zonohedra, Monohedra, Isozonohedra, and Otherhedra |url=https://doi.org/10.1007/s00283-010-9138-7 |journal=The Mathematical Intelligencer |language=en |volume=32 |issue=4 |pages=5–15 |doi=10.1007/s00283-010-9138-7 |hdl=1773/15593 |s2cid=120403108 |issn=1866-7414|hdl-access=free |url-access=subscription }} [http://faculty.washington.edu/moishe/branko/BG285%20Bilinski%20dodecahedron.pdf PDF]

Parallelogons have four or six sides, opposite sides that are equal in length, and 180-degree rotational symmetry around the center. A four-sided parallelogon is a parallelogram.

The three-dimensional analogue of a parallelogon is a parallelohedron. All faces of a parallelohedron are parallelogons.