The term "demiregular tessellation," also called a polymorph tessellation, has been used for several different collections of tessellations
by regular polygons . Traditional lists give 14
examples, but the lists do not all agree. Broader definitions, such as requiring
more than one group orbit of vertices
under the full symmetry group , allow infinitely
many tessellations (Aslaksen 2006, pp. 533-535).
A precisely defined related class consists of the 2-uniform tessellations . These are edge-to-edge tessellations
of the Euclidean plane by regular
polygons whose vertices form exactly two group orbits under the full symmetry
group . There are 20 such tessellations , illustrated
above. Krötenheerdt (1969) first enumerated these tessellations
(Grünbaum and Shephard 1986, pp. 65-67; Aslaksen 2006, p. 534).
See also Regular Tessellation ,
Semiregular Tessellation ,
Tessellation ,
Uniform Tessellation
Explore with Wolfram|Alpha
References Aslaksen, H. "In Search of Demiregular Tilings." In Proc. Bridges London: Mathematics, Music, Art, Architecture, Culture (Ed.
R. Sarhangi and J. Sharp). London, England: Tarquin Publications, pp. 533-536,
2006. https://archive.bridgesmathart.org/2006/bridges2006-533.html . Critchlow,
K. Order
in Space: A Design Source Book. Ghyka,
M. The
Geometry of Art and Life. Grünbaum,
B. and Shephard, G. C. Tilings
and Patterns. Krötenheerdt,
O. "Die homogenen Mosaike Wiss. Z.
Martin-Luther-Univ. Halle-Wittenberg, Math.-Natur. Reihe 18 , 273-290,
1969. Steinhaus, H. Mathematical
Snapshots, 3rd ed. Williams,
R. The
Geometrical Foundation of Natural Structure: A Source Book of Design. Referenced on Wolfram|Alpha Demiregular Tessellation
Cite this as:
Weisstein, Eric W. "Demiregular Tessellation."
From MathWorld https://mathworld.wolfram.com/DemiregularTessellation.html
Subject classifications More... Less...
-ter Ordnung in der euklidischen Ebene. I." Wiss. Z.
Martin-Luther-Univ. Halle-Wittenberg, Math.-Natur. Reihe 18, 273-290,
1969.Steinhaus, H.