Wedges

Any tromino (3 squares, joined edgewise) yields two ‘wedge’ shapes if you halve it by cutting the middle square diagonally. The wedges can be viewed as half-trominoes or as three 45-45-90 triangles aligned edgewise. Like the P-Pentomino, these wedges come in right- and left-handed forms which can tile themselves asymmetrically at a scale of 1/4.

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Side lengths are 1, 1, √2 and 2. So for full plane tiling the non-integral side must align with the non-integral side of an adjacent wedge. Above are the shapes possible when two identical wedges are arranged edgewise. The chart below shows the ways two enantiomorphic wedges can be arranged edgewise.

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Portland Zine Symposium 2016

 

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I premiered my latest book, “Three-Color Tiling,” at the Portland Zine Symposium on Saturday, July 9. This is another book from the analytical corner of my brain. The design is similar to “P-Pentomino Solutions” but the 46 patterns inside are in full color. The objective was to come up with a set of regular 3-color patterns in which the density of the three colors is equal. The patterns in this book are built on simple square or equilateral triangle units, but these generally combine with adjacent units as stripes, zigzags, chevrons, lozenges, and so forth. Some patterns are recognizable from common use in folk art and heraldry, but some of them seem novel. I applied a set of ship names to label the different designs, in part to memorialize the many hospital ships that were attacked and sunk as acts of war.

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