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The 4,460 decominos without holes comprise 44,600 unit squares. Thus, the largest square that can be tiled with distinct decominoes is at most 210 units on a side (210 squared is 44,100). Such a square containing 4,410 decominoes was constructed by Livio Zucca.
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8 decominoes have two axes of reflection symmetry, both aligned with the gridlines. Their symmetry group has four elements, the identity, two reflections and the 180° rotation. It is the
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1 decomino has two axes of reflection symmetry, both aligned with the diagonals. Its symmetry group is also the dihedral group of order 2 with four elements.
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22 decominoes have an axis of reflection symmetry at 45° to the gridlines. Their symmetry group has two elements, the identity and a diagonal reflection.
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aligned with the gridlines. Their symmetry group has two elements, the identity and the reflection in a line parallel to the sides of the squares.
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decominoes (the free decominoes comprise 195 with holes and 4,460 without holes). When reflections are considered distinct, there are 9,189
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195 decominoes have holes. This makes it trivial to prove that the complete set of decominoes cannot be
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The unique decomino with two axes of reflection symmetry, both aligned with the diagonals
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of order 2. Their symmetry group has two elements, the identity and the 180° rotation.
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decominoes. When rotations are also considered distinct, there are 36,446
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are not considered to be distinct shapes, there are 4,655 different
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of order 10; that is, a polygon in the plane made of 10 equal-sized
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202:(2nd ed.). Princeton, New Jersey: Princeton University Press.
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The 4,655 free decominoes can be classified according to their
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into a rectangle, and that not all decominoes can be
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102:73 decominoes have point symmetry, also known as
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85:. Their symmetry group consists only of the
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228:"Counting polyominoes: yet another attack"
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259:Iread.it: Maximal squares of polyominoes
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16:Geometric shape formed from ten squares
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113:of order 2, also known as the
92:90 decominoes have an axis of
35:connected edge to edge. When
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245:10.1016/0012-365X(81)90237-5
226:Redelmeier, D. Hugh (1981).
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81:4,461 decominoes have no
160:consisting of decominoes
148:consisting of decominoes
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158:geometric magic square
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232:Discrete Mathematics
146:self-tiling tile set
104:rotational symmetry
94:reflection symmetry
194:Golomb, Solomon W.
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136:Packing and tiling
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363:Higher dimensions
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411:Pseudo-polyomino
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115:Klein four-group
87:identity mapping
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75:symmetry groups
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238:(2): 191–203.
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111:dihedral group
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124:Unlike both
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57:decominoes.
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488:WikiProject
396:Polydrafter
370:Polyominoid
306:Polyominoes
199:Polyominoes
41:reflections
448:Snake cube
406:Polyiamond
180:References
130:nonominoes
126:octominoes
517:Polyforms
443:Soma cube
416:Polystick
391:Polyabolo
339:Heptomino
329:Pentomino
324:Tetromino
298:Polyforms
51:one-sided
37:rotations
29:polyomino
511:Category
458:Hexastix
375:Polycube
354:Decomino
349:Nonomino
344:Octomino
334:Hexomino
196:(1994).
83:symmetry
61:Symmetry
25:10-omino
21:decomino
464:Tantrix
453:Tangram
430:puzzles
401:Polyhex
319:Tromino
33:squares
27:, is a
498:Portal
471:Tetris
438:Blokus
384:Others
314:Domino
206:
166:packed
426:Games
170:tiled
55:fixed
23:, or
428:and
204:ISBN
172:.
128:and
46:free
39:and
240:doi
513::
236:36
234:.
230:.
218:^
156:A
144:A
77::
19:A
290:e
283:t
276:v
248:.
242::
212:.
117:.
89:.
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