|The symmetrical pairs|
|The 12 uniquely shaped quint pieces (pentominoes) can be paired in countless ways, but only the 52 pairs below are symmetrical with at least 2 unit edges of contact. The 52 pairs form 34 distinct shapes some can be built with more than one pair of quints, and some pairs of quints can form two or even three different symmetrical shapes.
Just for fun: Can you draw the 10 symmetrical pairs that have only 1 unit edge of contact?
It's fun to see what you can build with six pairs, as both two-dimensional and three-dimensional constructions. The Quintillions booklet illustrates several.
And here's how we package the Quintillions set. Can you spot all 5 symmetrical pairs, plus 3 symmetrical triplets? It was a happy coincidence that the W, our logo, ended up in the center.
This entire fascinating avenue of investigation became immortalized in an article Kate contributed to the Australian Game & Puzzle Design journal of the Queens University of Technology, published in Volume I, No. 1, June 2015, pp. 44-49. Read "Symmetrical Pentomino Pairs" here, courtesy of Cameron Browne, Editor-in-Chief.
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