Parallelogon

 ( Types Of Polygons ) 

In geometry, a parallelogon is a polygon with parallel opposite sides (hence the name) that can Tessellation a plane by translation (rotation is not permitted). 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.

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Two polygonal types Quadrilateral and hexagonal parallelogons each have varied geometric symmetric forms. They all have central inversion symmetry, order 2. Every convex parallelogon is a zonogon, but hexagonal parallelogons enable the possibility of nonconvex polygons.

Dih2, order 4

Dih4, order 8

Dih2, order 4

Dih6, order 12

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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.

+ Parallelogram tilings !colspan=2	1 length !colspan=2	2 lengths
Square p4 m (*442)	Rhombus cmm (2*22)	Rectangle pmm (*2222)	Parallelogram p2 (2222)

+ Hexagonal parallelogon tilings !1 length !colspan=2	2 lengths !colspan=2	3 lengths
hexagon p6 m (*632)	Elongated rhombus cmm (2*22)		Elongated parallelogram p2 (2222)

• The facts on file: Geometry handbook, Catherine A. Gorini, 2003, , p. 117
• (1987). 9780716711933, W. H. Freeman. . ISBN 9780716711933
  list of 107 isohedral tilings, p. 473-481

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External links

• Fedorov's Five Parallelohedra

• The surprising 3D parallelo-hexagon at Dynamic Geometry Sketches

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