Kate Jones
The theme of my art submission is "Imagine it and build it", the amazing combinatorial diversity of Math as Art. The poster shows a variety of designs created with 5 different octiamonds (shapes made of 8 equilateral triangles) published by Kadon as "Handy-Octs". They cannot form a convex shape and can form only very few symmetrical figures with 3, 4, and 5 pieces. No two can form a symmetry. Build them into recognizable shapes (art), and fit them into convex “envelopes” with minimal spaces and stable structures (space packing). The poster shows several samples of diverse subjects. Why these 5 octiamonds? How many ways can you choose 5 from the total of 66? See www.gamepuzzles.com/handy-octs.htm and www.gamepuzzles.com/esspoly.htm#OR
Images of designs formed with five octiamonds that are named for what they appear to resemble, such as Bird on Roof, Swan, Elephant, Curious Duck, Glamor Girl, etc. This amazing combinatorial diversity with a mere five pieces turns Math into Art, a unique intellectual pleasure like meditation, exercising both logic and creativity, math and imagination. The five building blocks have unique characteristics of their own, such as NOT being able to form symmetrical concepts in pairs, though a few exist with 3, 4, and 5. We thank George Sicherman and his program for deriving proofs and some results, specifically that no convex shape is possible with any combination. Convex "envelopes" with a minimum number of holes are interesting. Win prizes!