Polyform Tiling

The slabs made a most intricate and fascinating design, but a thoroughly unobtrusive one, unless one paid deliberate attention to it.

—Carlos Castaneda, The Second Ring of Power

The tiling problem is to join copies of one or more polyforms to make a given polyform.

	Kiteless Didoms. Form shapes with the set of 12 didoms, omitting the kite didom.
	Scaled Polydom Tetrads. Join four similar polydoms so that each borders the other three.
	Polydom Irreptiling. Dissect a polydom into smaller copies of it, not necessarily equal.
	Didom Kites and Bricks. Livio Zucca's problem of tiling a rectangle with didom kites and dominoes.
	A Counterexample To Livio Zucca's Island Conjecture. Make a polydom island in the shape of a polyomino that cannot be tiled with dominoes.
	Convex Figures with Didom Pairs. Make a convex polydom with copies of two didoms.
	Convex Figures with Didom Triplets. Make a convex polydom with copies of three didoms.
	Convex Shapes from the 13 Didoms. Make a convex polydom with the 13 didoms, including the Kite Didom.
	Inflated Didoms. Make a convex polydom with the 13 didoms, including the Kite Didom, enlarging some.
	Tiling the Owen Dodecagon With Three Didoms. Make an almost regular dodecagon with copies of the 13 didoms.

Strong Surround Numbers for Polycairos. With how few copies of a polycairo can it completely enclose itself?

Strong Surround Numbers for Polykites. With how few copies of a polykite can it completely enclose itself?

	Contiguous Partridge Tilings. Use 1 shape at scale 1, 2 at scale 2, and so on up to n at scale n, to form a scaled copy of the shape in which equal tiles are contiguous.
	Contiguous Reverse Partridge Tilings. Use 1 shape at scale n, 2 at scale n−1, and so on up to n at scale 1, to form a scaled copy of the shape in which equal tiles are contiguous.
	Lovebirds Tilings. Use 2 copies of a shape at scale 1, 4 at scale 2, and so on up to 2n at scale n, to form two scaled copies of the shape.

Col. George Sicherman [ HOME | MAIL ]