#FIG 3.2 Portrait Center Inches Letter 100.00 Single -2 1200 2 6 1125 2325 4875 2475 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 1200 2400 75 75 1200 2400 1275 2400 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 1800 2400 75 75 1800 2400 1875 2400 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 2400 2400 75 75 2400 2400 2475 2400 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 3000 2400 75 75 3000 2400 3075 2400 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 3600 2400 75 75 3600 2400 3675 2400 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 4200 2400 75 75 4200 2400 4275 2400 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 4800 2400 75 75 4800 2400 4875 2400 -6 6 1125 3525 4875 3675 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 1200 3600 75 75 1200 3600 1275 3600 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 1800 3600 75 75 1800 3600 1875 3600 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 2400 3600 75 75 2400 3600 2475 3600 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 3000 3600 75 75 3000 3600 3075 3600 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 3600 3600 75 75 3600 3600 3675 3600 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 4200 3600 75 75 4200 3600 4275 3600 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 4800 3600 75 75 4800 3600 4875 3600 -6 6 1125 2925 4875 3075 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 1200 3000 75 75 1200 3000 1275 3000 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 1800 3000 75 75 1800 3000 1875 3000 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 2400 3000 75 75 2400 3000 2475 3000 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 3000 3000 75 75 3000 3000 3075 3000 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 3600 3000 75 75 3600 3000 3675 3000 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 4200 3000 75 75 4200 3000 4275 3000 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 4800 3000 75 75 4800 3000 4875 3000 -6 6 1125 4125 4875 4275 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 1200 4200 75 75 1200 4200 1275 4200 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 1800 4200 75 75 1800 4200 1875 4200 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 2400 4200 75 75 2400 4200 2475 4200 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 3000 4200 75 75 3000 4200 3075 4200 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 3600 4200 75 75 3600 4200 3675 4200 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 4200 4200 75 75 4200 4200 4275 4200 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 4800 4200 75 75 4800 4200 4875 4200 -6 6 1125 4725 4875 4875 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 1200 4800 75 75 1200 4800 1275 4800 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 1800 4800 75 75 1800 4800 1875 4800 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 2400 4800 75 75 2400 4800 2475 4800 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 3000 4800 75 75 3000 4800 3075 4800 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 3600 4800 75 75 3600 4800 3675 4800 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 4200 4800 75 75 4200 4800 4275 4800 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 4800 4800 75 75 4800 4800 4875 4800 -6 6 1125 5325 4875 5475 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 1200 5400 75 75 1200 5400 1275 5400 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 1800 5400 75 75 1800 5400 1875 5400 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 2400 5400 75 75 2400 5400 2475 5400 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 3000 5400 75 75 3000 5400 3075 5400 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 3600 5400 75 75 3600 5400 3675 5400 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 4200 5400 75 75 4200 5400 4275 5400 1 3 0 1 0 7 50 0 0 0.000 1 0.0000 4800 5400 75 75 4800 5400 4875 5400 -6 6 675 600 2400 1800 2 2 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 5 1200 600 2400 600 2400 1800 1200 1800 1200 600 4 2 0 50 0 0 26 0.0000 4 270 435 1125 1350 S=\001 -6 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 1200 3300 4800 3300 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 1200 3900 4800 3900 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 1200 4500 4800 4500 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 1200 5100 4800 5100 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 1200 2700 4800 2700 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 1500 2400 1500 5400 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 2100 2400 2100 5400 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 2700 2400 2700 5400 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 3900 2400 3900 5400 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 4500 2400 4500 5400 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 3300 2400 3300 5400 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 6000 2400 6000 5400 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 6600 2400 6600 5400 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 7200 2400 7200 5400 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 7800 2400 7800 5400 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 8400 2400 8400 5400 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 5400 3000 9000 3000 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 5400 3600 9000 3600 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 5400 4200 9000 4200 2 1 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 2 5400 4800 9000 4800 2 2 0 2 0 7 50 0 -1 0.000 0 0 -1 0 0 5 1200 2400 4800 2400 4800 5400 1200 5400 1200 2400 2 2 0 2 0 7 50 0 -1 0.000 0 0 -1 0 0 5 5400 2400 9000 2400 9000 5400 5400 5400 5400 2400 2 2 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 5 4200 900 4800 900 4800 1500 4200 1500 4200 900 4 2 0 50 0 0 26 0.0000 4 300 1020 4125 1350 1/2 S=\001 4 1 0 50 0 0 16 0.0000 4 210 2235 3000 6000 positions labeled with 1\001 4 1 0 50 0 0 16 0.0000 4 210 1275 7275 6000 a 1/2 S-tiling\001 4 1 0 50 0 0 16 0.0000 4 210 5565 5250 7020 with label 1 contained in any translate of the open set 1/2S,\001 4 1 0 50 0 0 16 0.0000 4 210 5190 5250 6750 For this particular 1/2S-tiling there are no lattice points\001 4 1 0 50 0 0 16 0.0000 4 210 6150 5250 7290 but each translate has 4 positions labeled with 1 on the boundary.\001