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  About site: http://www.monmouth.com/~colonel/xpoly/xpoly.html

Title: Math/Recreations/Polyominoes - Polyiamond Exclusion Colonel Sicherman asks what fraction of the triangles need to be removed from a regular triangular tiling of the plane, in order to make sure that the remaining triangles contain no copy of a given po
Polyiamonds Mathforum. This Geometry problem of the week asks whether a six-point star can be dissected to form eight distinct hexiamonds.

Polyomino_and_Polyhex_Tiling Joseph Myer's tables of polyominoes and of polyomino tilings, in Postscript format.

Polyomino_Applet Wil Laan's applet searches for solution of packing hexominoes into more than 45 different shapes.[Java]

Polyomino_Enumeration K. S. Brown examines the number of polyominoes up to order 12 for various cases involving rotation or reflections. Equations linking the cases are proposed.

Polyomino_Fuzion_Game Puzzles using pentominoes and hexominoes. Fuzion, game that designs and (semi-)automatically finds solutions. Links.

Polyomino_Tiling Joseph Myers classifies the n-ominoes up to n=15 according to how symmetrically they can tile the plane.

Polyominoes Describes a numerical invariant that can be used to classify polyominoes.

Polyominoes Introduction to Tetrominoes, Pentominoes, Hexominoes, Heptominoes, Octominoes, Fixed (translation only) Polyominoes. Numerous Links.

Polyominoes__Theme_and_Variations Jankok presents information about filling rectangles, other polygons, boxes, etc., with dominoes, trominoes, tetrominoes, pentominoes, solid pentominoes, hexiamonds, and whatever else people have inve

Polyominoids Jorge Luis Mireles Jasso presents connected sets of squares in a 3d cubical lattice. Includes a Java applet as well as non-animated description.

Polypolygon_Tilings S. Dutch discusses polyominoes, poliamonds, and polypolygons with special attention to tiling characteristics.

Primes_of_a_14-omino Michael Reid shows that a 3x6 rectangle with a 2x2 bite removed can tile a (much larger) rectangle. It is open whether it can do this using an odd number of copies.

Puzzle_Fun Newsletter edited by Rodolfo Kurchan about pentominoes and other math problems.


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    Polyominoes Describes a numerical invariant that can be used to classify polyominoes.
    Polyominoes Introduction to Tetrominoes, Pentominoes, Hexominoes, Heptominoes, Octominoes, Fixed (translation only) Polyominoes. Numerous Links.
    Polyominoes__Theme_and_Variations Jankok presents information about filling rectangles, other polygons, boxes, etc., with dominoes, trominoes, tetrominoes, pentominoes, solid pentominoes, hexiamonds, and whatever else people have inve
    Polyominoids Jorge Luis Mireles Jasso presents connected sets of squares in a 3d cubical lattice. Includes a Java applet as well as non-animated description.
    Polypolygon_Tilings S. Dutch discusses polyominoes, poliamonds, and polypolygons with special attention to tiling characteristics.
    Primes_of_a_14-omino Michael Reid shows that a 3x6 rectangle with a 2x2 bite removed can tile a (much larger) rectangle. It is open whether it can do this using an odd number of copies.
    Puzzle_Fun Newsletter edited by Rodolfo Kurchan about pentominoes and other math problems.
    Random_Domino_Tiling_of_an_Aztec_Diamond Matthew Blum's undergraduate project demonstrates the properties of random domino tiling of an Aztec diamond. Interactive graphics display included.
    Rectifiable_Polyomino Karl Dahlke explains and demonstrates tiling. Includes C-program source.
    Schröder_Triangles,_Paths,_and_Parallelogram_Polyominoes A paper on their enumeration by Elisa Pergola and Robert A. Sulanke.
    Six_Squares_Problem This Geometry Forum problem of the week asks for the number of different hexominoes, and for how many of them can be folded into a cube.
    Solomon_W__Golomb Home Page of the inventor of polyominoes. Includes biography, black and white picture, research interests and publications list.
    The_Soma_Cube Soma-solving program in QBASIC by Courtney McFarren.
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    The_Three_Dimensional_Polyominoes_of_Minimal_Area L. Alonso and R. Cert's abstract of a paper published in vol. 3 of the Elect. J. Combinatorics. Full paper available in different formats (.pdf, postscript, tex etc).
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    Unbalanced_Anisohedral_Tiling Joseph Myers and John Berglund found a polyhex that must be placed in two different ways in a tiling of a plane, such that one placement occurs twice as often as the other.
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    What_is_a_Golygon? Harry Smith describes Dr. Dewdney's article in the July 1990 Scientific American's Mathematical Recreations column.
    Xominoes Livio Zucca finds a set of markings for the edges of a square that lead to exactly 100 possible tiles, and asks how to fit them into a 10x10 grid.
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Colonel

Sicherman

asks

what

fraction

of

the

triangles

need

to

be

removed

from

a

regular

triangular

tiling

of

the

plane,

in

order

to

make

sure

that

the

remaining

triangles

contain

no

copy

of

a

given

po

http://www.monmouth.com/~colonel/xpoly/xpoly.html

Polyiamond Exclusion 2008 December

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Colonel Sicherman asks what fraction of the triangles need to be removed from a regular triangular tiling of the plane, in order to make sure that the remaining triangles contain no copy of a given po

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