|Handy-Octs a unique 5-piece art puzzle|
Here are five different "octiamonds" (shapes made of 8 equilateral triangles). Let's call them L, J, V, M, and Y. They cannot form a convex shape, and only a very few symmetrical figures are possible with 3, 4, and 5 pieces. No two can form a symmetry. Yet you can form them into countless recognizable shapes (art), and fit them into convex "envelopes" with minimal spaces and stable structures (space packing). We show some samples of each kind below to give you an idea of their versatility.
Why these five octiamonds? Because they were the survivors of a lengthy evolutionary solving process. In how many ways could 5 different octiamonds have been selected from the total of 66? Email your results to firstname.lastname@example.org.
George Sicherman found at least 4 symmetrical solutions with all 5 pieces (one is shown at right), several 3- and 4-piece symmetries, and also proved that convex shapes are impossible with this group.
Convex "envelopes", however, can hold all 5 handy-octs with minimal spaces left over. Below we show from 3 to 8 unit triangle holes. Can you find others? Can you find one with only 2 extra spaces? Only 1? Send us your new solutions and win a prize.
Imagine it and build it... (hover over images for description)
|Back to Octiamond Ring|