Parallelogon
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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). 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.
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). 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.
Geometric variations
A parallelogram can tile the plane as a distorted square tiling while a hexagonal parallelogon can tile the plane as a distorted regular hexagonal tiling.
References
The facts on file: Geometry handbook, Catherine A. Gorini, 2003, , p. 117 list of 107 isohedral tilings, p. 473-481
External links
Fedorov's Five Parallelohedra The surprising 3D parallelo-hexagon at Dynamic Geometry Sketches
Text derived from https://en.wikipedia.org/w/index.php?oldid=1345994066 under CC BY-SA 4.0; modifications have been made.