Kate Jones
I create and make original tiling sets (playable art) of geometric combinatorial concepts. Each set can be rearranged to form amazing designs, symmetries and combinations. Each set has its own unique mathematical properties. We produce them in lasercut acrylic in vibrant colors, where the colors themselves are part of the character of each set. Designed in framed holding trays for display as art on easels. They are intriguing to play with, with simpler models suitable even for children. Solutions can be found by hand and also lend themselves to computer searches. Many of my designs are members of and can be plotted on the grids of the 17 classic symmetry groups.
36 different uniquely posed teddybears, thematically related to DaVinci's Vitruvean Man, fill a 6x6 Latin Square with three conditions: each row and column contains 6 colors and 6 arms positions and at least one each of the four different leg positions; further, 8 vertical and 10 horizontal 2x3 rectangles also contain all 6 colors. Six bears are self-symmetric; the remaining 30 form 15 pairs of mirror twins that can switch places when flipped, giving 2^15 or 32,768 placements. Top of tray is cut to the 36 contours; back has 36 circles where 36! placements fit. Order-6 Latin Squares are stubborn: they won't allow all different colors on every diagonal. The 6 duplicates shown are the best we can do. For fun, the bears smile on both sides.
45 thin and 45 thick Penrose rhombs (based on the golden ratio) show four right triangles each, inlaid with every combination of 3 colors. Arrange them in countless beautiful patterns by matching the colors. Shown is a grand decagon with the optical illusion of a rhombic icosahedron. Based on a concept by Ward Hollins, developed and designed by Kate Jones. A framed tray holds this design as an ever-changing artwork with fitted see-through cover when displayed. The color theme derives from MacMahon's Three-Color Squares (1923) where all joined edges match and the entire perimeter is a single color. It is not known how many solutions exist. Note that the solution shown can rotate the 5 thin 3x3 sections and the star will disappear.