Abstract: Families of rhombus-based two-zoomorph variably assemblable tile sets wherein a single amphographic line delineates different parts of one zoomorph and different parts of a second and different zoomorph as well, and may similarly delineate further fatter or skinnier zoomorphs. All or some of these may, in conjunction with one another, tile the plane in an infinite number of different and interesting ways. These tiles and tilings and patches of tiles may be used in puzzles, in games, for teaching certain aspects of geometry, or for the decoration of fabrics or other surfaces.

Abstract: Single-member sets of zoomorphic tiles, in which any single tile, if duplicated, can tile the plane in periodic ways, or, with duplicates of its mirror image, in either periodic or non periodic ways, and which can also form tilings of the plane in conjunction with duplicates of any other appropriately sized but differently shaped embodiment or embodiments of the invention. The diverse and variable arrangements show vertices at which 3, 4, 5, and 6 tiles meet. These tiles, tilings, patches and rosettes of tiles may be used in puzzles, games and other recreations, for teaching certain aspects of geometry, for various purposes in conjunction with computers, for the decoration of fabrics or other surfaces, for the shape of food items such as cookies, or for other uses to which tiles or tilings may be put.

Abstract: A set of tiles for covering a surface is composed of eight distinct shapes that are insect-like in that they are bilaterally symmetrical and have six leg-like projections. Each sort of tile will fit together with another tile of the set in an average of nine different ways. The tiles may be assembled jig-saw-puzzle fashion in an infinite number of distinct tilings. Ten different subsets of the eight insect-like or beetle-like tiles will tile the plane, some in several highly distinctive manners. The many and variable tiling patterns have considerable aesthetic appeal. They may be used as fabric prints, wall coverings, and the like, or as jewelry designs, or as highly efficient patterns for shaped cookies, etc. The tiles of the invention may also be used as teaching aids, or as puzzle pieces in an unlimited number of different puzzles of every level of simplicity or difficulty.