Levitov Block
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*Edit:* I Should Warn You That The Colorful Pictures Were Pulled Out Of My Ph.D. Thesis. The Files I Posted Are A Slightly Different Design - A Slightly Superior One, From A Practical Point Of View; The New Blocks Stack Better. Moreover, To Duplicate These Pictures Exactly Would Take Like 400 Red Levitov Blocks And 400 Blue Ones, Or Something. Of Course, If Someone Actually Does This, I'D Be Very Happy! But I Don'T Want To Burn Through Quite That Much Filament, Myself. These Blocks Are A Concrete Realization Of The Height Function Of A Domino Tiling. They'Re Kind Of Similar To Lego, But Their (Admittedly Somewhat Strange) Connectors Ensure That They Can Only Be Stacked Up So That, When Viewed From Above, You See A Domino Tiling Of The Plane. Adding/Removing A Block Swaps Two Side-By-Side Horizontal Dominos For Two Vertical Ones. I'Ve Attached A Couple Pictures Of These Blocks Which I Pulled Out Of My Ph.D. Thesis. I Sure Wish I Had A Big Set Of These During My Ph.D. - As Is, I Had To Make Do With Lego. References: Levitov, Ls. The Rvb Model As The Problem Of The Surface Of A Quantum Crystal. Jetp Letters 50 (10),469-472,1989. Elkies, Kuperberg, Larsen, Propp, "Alternating Sign Matrices And Domino Tilings", Journal Of Algebraic Combinatorics Vol 1, #2, Pp. 111-132 And Vol 1, #3, Pp 219-234; Preprint At Http://Arxiv.Org/Pdf/Math.Co/9201305).
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