# 2–4–6–8, All Quadrilaterals Tesselate! **URL:** https://scanalyst.fourmilab.ch/t/2-4-6-8-all-quadrilaterals-tesselate/353 **Category:** Context **Tags:** tesselation, geometry **Created:** [12 November 2021 13:16 UTC](https://scanalyst.fourmilab.ch/t/2-4-6-8-all-quadrilaterals-tesselate/353 "2021-11-12T13:16:33Z") **Posts on this page:** 1 **Page:** 1
### Author: ![johnwalker](https://scanalyst.fourmilab.ch/user_avatar/scanalyst.fourmilab.ch/johnwalker/32/17415_2.png) [@johnwalker](https://scanalyst.fourmilab.ch/u/johnwalker) #### Post date: [12 November 2021 13:16 UTC](https://scanalyst.fourmilab.ch/t/2-4-6-8-all-quadrilaterals-tesselate/353/1 "2021-11-12T13:16:34Z")
[![](https://scanalyst.fourmilab.ch/uploads/default/original/2X/a/a3aeba34c8edc54d41239c2f7871a83939897714.jpeg "Tessellation Is Easier Than You Think") ](https://www.youtube.com/watch?v=eFXxTTaC_zY) [More formally](https://en.wikipedia.org/wiki/Tessellation#Tessellations_with_polygons), > Any triangle or [quadrilateral](https://en.wikipedia.org/wiki/Quadrilateral) (even [non-convex](https://en.wikipedia.org/wiki/Concave_polygon)) can be used as a prototile to form a monohedral tessellation, often in more than one way. Copies of an arbitrary [quadrilateral](https://en.wikipedia.org/wiki/Quadrilateral) can form a tessellation with translational symmetry and 2-fold rotational symmetry with centres at the midpoints of all sides. For an asymmetric quadrilateral this tiling belongs to [wallpaper group p2](https://en.wikipedia.org/wiki/Wallpaper_group#Group_p2). As [fundamental domain](https://en.wikipedia.org/wiki/Fundamental_domain) we have the quadrilateral. Equivalently, we can construct a [parallelogram](https://en.wikipedia.org/wiki/Parallelogram) subtended by a minimal set of translation vectors, starting from a rotational centre. We can divide this by one diagonal, and take one half (a triangle) as fundamental domain. Such a triangle has the same area as the quadrilateral and can be constructed from it by cutting and pasting.