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Parallelogon

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.

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.

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