Parallelogons have an even number of sides and opposite sides that are equal in length. A less obvious corollary is that parallelogons can only have either four or six sides;[1] Parallelogons have 180-degree rotational symmetry around the center.
A four-sided parallelogon is called a parallelogram.
The faces of a parallelohedron (the three dimensional analogue) are called parallelogons.[2]
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.
^ a bAleksandr Danilovich Alexandrov (2005) [1950]. Convex Polyhedra. Translated by N.S. Dairbekov; S.S. Kutateladze; A.B. Sosinsky. Springer. p. 351. ISBN 3-540-23158-7. ISSN 1439-7382.
^ a bGrünbaum, Branko (2010-12-01). "The Bilinski Dodecahedron and Assorted Parallelohedra, Zonohedra, Monohedra, Isozonohedra, and Otherhedra". The Mathematical Intelligencer. 32 (4): 5–15. doi:10.1007/s00283-010-9138-7. hdl:1773/15593. ISSN 1866-7414. S2CID 120403108. PDF
The facts on file: Geometry handbook, Catherine A. Gorini, 2003, ISBN 0-8160-4875-4, p. 117
Grünbaum, Branko; Shephard, G. C. (1987). Tilings and Patterns. New York: W. H. Freeman. ISBN 0-7167-1193-1. list of 107 isohedral tilings, p. 473-481