Octomino: Difference between revisions
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Removed octomino figure - technically inaccurate (two are heptominos). Also removed symmetry group description as it's dependant on the figure. |
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[[Image:All 369 free octominoes.svg|thumb|400px|The 369 free octominoes]] |
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An '''octomino''' (or '''8-omino''') is a [[polyomino]] of order 8, that is, a [[polygon]] in the [[plane (mathematics)|plane]] made of 8 equal-sized [[square (geometry)|square]]s connected edge-to-edge. When [[rotation]]s and [[Reflection (mathematics)|reflection]]s are not considered to be distinct shapes, there are [[369]] different "free" octominoes. |
An '''octomino''' (or '''8-omino''') is a [[polyomino]] of order 8, that is, a [[polygon]] in the [[plane (mathematics)|plane]] made of 8 equal-sized [[square (geometry)|square]]s connected edge-to-edge. When [[rotation]]s and [[Reflection (mathematics)|reflection]]s are not considered to be distinct shapes, there are [[369]] different "free" octominoes. |
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The figure shows all possible octominoes, coloured according to their [[symmetry group]]s: |
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*316, coloured grey, have no [[symmetry]]. Their symmetry groups consist only of the [[identity mapping]] |
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*23, coloured red, have an axis of [[mirror symmetry]] aligned with the gridlines. Their symmetry groups have two elements, the identity and a reflection in a line parallel to the sides of the squares. |
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*7, coloured green, have an axis of mirror symmetry at 45° to the gridlines. Their symmetry groups have two elements, the identity and a diagonal reflection. |
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*17, coloured blue, have point symmetry, also known as [[rotational symmetry]] of order 2. Their symmetry groups have two elements, the identity and a 180° rotation. |
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*5, coloured purple, have two axes of mirror symmetry, both aligned with the gridlines. Their symmetry groups have four elements. |
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*1, also coloured purple, has rotational symmetry of order 4. Its symmetry group has four elements. |
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{{Polyforms}} |
{{Polyforms}} |
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Revision as of 11:15, 7 June 2009
An octomino (or 8-omino) is a polyomino of order 8, that is, a polygon in the plane made of 8 equal-sized squares connected edge-to-edge. When rotations and reflections are not considered to be distinct shapes, there are 369 different "free" octominoes.
| Polyominoes | |
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| Higher dimensions | |
| Others | |
| Games and puzzles | |
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