don steward
mathematics teaching 10 ~ 16

Sunday, 15 December 2013

pentomino tessellations

tessellations created of shapes made out of 'units' composed of a number of squares (the 2 triominoes, 5 quadrominoes (or tetrominoes), 12 pentominoes...) can be interesting to complete and then analyse for their various regularities
such as:
  • symmetries of the resulting pattern
  • a parallelogram or 'overlay' that shows the background structure of the tessellation
  • vectors that are used to move the 'units' to create the tessellation

different tessellations of the same triomino

different tessellations of the same pentomino

ways to start a pentomino tessellation
one way to create a tessellation with this pentomino
joining some corresponding corners gives a parallelogram

moving along the lines of the tessellation between the corners of the parallelogram - what do you notice?

see also

and this

textile art by J Bruce Wilcox:

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