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27
Article Polyominoes and Polyiamonds as Fundamental Domains of Isohedral Tilings with Rotational Symmetry
, 2011
"... symmetry ..."
Maximal and Minimal Polyiamonds
, 2002
"... The minimum perimeter of an npolyiamond is whichever of ⌈√(6n)⌉ or ⌈√(6n)⌉ + 1 has the same parity as n. To prove this result, we first obtain a lower bound on the perimeter by considering maximal polyiamonds (i.e., polyiamonds with a give ..."
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The minimum perimeter of an npolyiamond is whichever of ⌈√(6n)⌉ or ⌈√(6n)⌉ + 1 has the same parity as n. To prove this result, we first obtain a lower bound on the perimeter by considering maximal polyiamonds (i.e., polyiamonds with a
Tiling rectangles with holey polyominoes
, 2014
"... We present a new type of polyominoes that can have transparent squares (holes). We show how these polyominoes can tile rectangles and we categorise them according to their tiling ability. We were able to categorise all but 7 polyominoes with 5 or fewer visible squares. 1 ..."
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We present a new type of polyominoes that can have transparent squares (holes). We show how these polyominoes can tile rectangles and we categorise them according to their tiling ability. We were able to categorise all but 7 polyominoes with 5 or fewer visible squares. 1
Hinged Dissection of Polyominoes and Polyforms
"... A hinged dissection of a set of polygons S is a collection of polygonal pieces hinged together at vertices that can be rotated into any member of S. We present a hinged dissection of all edgetoedge gluings of n congruent copies of a polygon P that join corresponding edges of P. This construction u ..."
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uses kn pieces, where k is the number of vertices of P. When P is a regular polygon, we show how to reduce the number of pieces to ⌈k/2⌉(n − 1). In particular, we consider polyominoes (made up of unit squares), polyiamonds (made up of equilateral triangles), and polyhexes (made up of regular hexagons
Combinatorially regular polyomino tilings, preprint, available from http://www.math.vt.edu/people/floyd
"... Abstract. Let T be a regular tiling of R 2 which has the origin 0 as a vertex, and suppose that ϕ: R 2 → R 2 is a homeomorphism such that i) ϕ(0) = 0, ii) the image under ϕ of each tile of T is a union of tiles of T, and iii) the images under ϕ of any two tiles of T are equivalent by an orientation ..."
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Cited by 1 (1 self)
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by an orientationpreserving isometry which takes vertices to vertices. It is proved here that there is a subset Λ of the vertices of T such that Λ is a lattice and ϕΛ is a group homomorphism. The tiling ϕ(T) is a tiling of R 2 by polyiamonds, polyominos, or polyhexes. These tilings occur often as expansion
DOMAINS OF ISOHEDRAL TILINGS WITH ROTATIONAL SYMMETRY (Submitted to International Journal of Computational
, 2011
"... ar ..."
Hinged dissection of polyominoes and polyforms
 Computational Geometry: Theory and Applications
, 2005
"... ..."
Enumeration of generalized polyominoes
, 2005
"... As a generalization of polyominoes we consider edgetoedge connected nonoverlapping unions of regular kgons. For n ≤ 4 we determine formulas for the number ak(n) of generalized polyominoes consisting of n regular kgons. Additionally give a table of the numbers ak(n) for small k and n obtained by ..."
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As a generalization of polyominoes we consider edgetoedge connected nonoverlapping unions of regular kgons. For n ≤ 4 we determine formulas for the number ak(n) of generalized polyominoes consisting of n regular kgons. Additionally give a table of the numbers ak(n) for small k and n obtained
Fractal Tilings Based on Dissections of Polyhexes
 in Renaissance Banff, Mathematics, Music, Art, Culture Conference Proceedings, 2005, edited by Reza Sarhangi and
, 2005
"... Polyhexes, shapes made up of regular hexagons connected edgetoedge, provide a rich source of prototiles for edgetoedge fractal tilings. Numerous examples are given of fractal tilings with 2fold and 3fold rotational symmetry based on prototiles derived by dissecting polyhexes with 2fold and 3 ..."
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Polyhexes, shapes made up of regular hexagons connected edgetoedge, provide a rich source of prototiles for edgetoedge fractal tilings. Numerous examples are given of fractal tilings with 2fold and 3fold rotational symmetry based on prototiles derived by dissecting polyhexes with 2fold and 3
Forcing nonperiodicity with a single tile
 The Mathematical Intelligencer
, 2012
"... It is easy to create nonperiodic tesselations of the plane composed of one or a few types of tiles. In most cases, however, the tiles employed can also be used to create simpler, periodic patterns. It is much more difficult to find shapes, or “prototiles, ” that can fill space only by making a nonpe ..."
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Cited by 2 (0 self)
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It is easy to create nonperiodic tesselations of the plane composed of one or a few types of tiles. In most cases, however, the tiles employed can also be used to create simpler, periodic patterns. It is much more difficult to find shapes, or “prototiles, ” that can fill space only by making a
Results 1  10
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27