The compatibility problem is to find a figure that can be tiled with each of a set of polyforms. Giovanni Resta's website Polypolyominoes (Polipolimini in Italian) presents compatibility results for polyominoes with as many as 10 cells. It is the Web's main resource for polyomino compatibility.
Since Resta assembled and posted his results, I have found a few new or smaller solutions. It is hard for Resta to add or change solutions in his compact web graphic format, so I present my solutions here instead. Resta shows some of my solutions on his main page and his individual pages.
I do not claim to have found all possible new and improved solutions. If you find others, please write!
6AC = 5Y | 6AE = 5U | 6BG = 5X! | 6BH = 5Z |
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5 / 6 | 40 / 48 | 120 / 144 | 40 / 48 |
6AX = 6AZ! |
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68 / 68 |
7BX = 4Q | 7CY = 4N | 7DY = 4T! | 7EB = 4Q |
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16 / 28 | 32 / 56 | 32 / 56 | 32 / 56 |
7CU = 4Q! | |||
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128 / 224 |
7AP = 5N! | 7AV = 5L! | 7AY = 5I | 7BN = 5I |
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70 / 98 | 40 / 56 | 20 / 28 | 30 / 42 |
7AI = 5U | 7AV = 5P! | 7AY = 5U | 7BL = 5T |
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30 / 42 | 40 / 56 | 30 / 42 | 30 / 42 |
7CD = 5U | 7CW = 5V | 7CX = 5V | 7DA = 5V |
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30 / 42 | 30 / 42 | 20 / 28 | 20 / 28 |
7DF = 5T | 7DG = 5T | 7DN = 5T! | 7DO = 5V |
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30 / 42 | 30 / 42 | 40 / 56 | 30 / 42 |
7DR = 5T | 7DW = 5U | 7DX = 5T | |
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30 / 42 | 20 / 28 | 30 / 42 |
7AN = 5Z | 7AT = 5Z | 7BL = 5Z | 7CB = 5Z |
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30 / 42 | 20 / 28 | 30 / 42 | 20 / 28 |
7CH = 5W | 7CJ = 5Z | 7CQ = 5X! | |
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30 / 42 | 30 / 42 | 100 / 140 | |
7CV = 5Z | 7DE = 5Z! | 7DL = 5Y | 7DQ = 5Z! |
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30 / 42 | 40 / 56 | 20 / 28 | 50 / 70 |
8KD = 3I | 8MY = 3I! |
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24 / 64 | 66 / 176 |
8DP = 4I |
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28 / 56 |
8LZ = 4N! |
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48 / 96 |
8BV = 4Q! | 8DM = 4Q! | 8JA = 4Q! |
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56 / 112 | 52 / 104 | 44 / 88 |
8KQ = 4Q! | 8MO = 4Q | 8MP = 4Q |
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28 / 56 | 28 / 56 | 24 / 48 |
8AF = 5F! | 8AF = 5V! | 8AI = 5Z! | 8AK = 5T! | |
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60 / 96 | 20 / 32 | 20 / 32 | 20 / 32 | |
8AL = 5T! | 8AN = 5T! | 8AN = 5W! | 8AN = 5Z! | |
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20 / 32 | 40 / 64 | 20 / 32 | 20 / 32 | |
8AQ = 5T! | 8AQ = 5V! | 8AR = 5T! | ||
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40 / 64 | 20 / 32 | 20 / 32 | ||
8AZ = 5L! | 8AZ = 5Z! | 8BD = 5P! | ||
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20 / 32 | 20 / 32 | 20 / 32 | ||
8BD = 5Z! | 8BF = 5V! | 8BH = 5V! | 8BQ = 5V! | |
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20 / 32 | 20 / 32 | 20 / 32 | 20 / 32 | |
8BR = 5T! | 8BR = 5V! | 8BX = 5V! | 8BZ = 5U! | 8CA = 5Z! |
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20 / 32 | 20 / 32 | 20 / 32 | 20 / 32 | 20 / 32 |
8CB = 5T! | 8CD = 5I! | 8CE = 5W! | 8CH = 5T! | |
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40 / 64 | 40 / 64 | 20 / 32 | 20 / 32 | |
8CI = 5V! | 8CJ = 5T! | 8CK = 5T! | 8CN = 5Z! | 8CO = 5T! |
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20 / 32 | 20 / 32 | 20 / 32 | 20 / 32 | 20 / 32 |
8CR = 5W! | 8CU = 5U! | 8CU = 5V! | ||
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40 / 64 | 40 / 64 | 20 / 32 | ||
8CU = 5W! | 8CW = 5Z! | 8CZ = 5T! | ||
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40 / 64 | 20 / 32 | 20 / 32 | ||
8DA = 5W! | 8DE = 5N! | 8DF = 5Z! | 8DG = 5U! | |
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40 / 64 | 10 / 16 | 20 / 32 | 20 / 32 | |
8DH = 5U! | 8DI = 5V! | 8DL = 5U! | 8DM = 5V! | |
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20 / 32 | 40 / 64 | 20 / 32 | 40 / 64 | |
8DO = 5T! | 8DO = 5U! | 8DQ = 5U! | ||
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40 / 64 | 20 / 32 | 40 / 64 | ||
8DR = 5T! | 8DU = 5U! | 8DV = 5V! | 8DX = 5Z! | |
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40 / 64 | 20 / 32 | 20 / 32 | 20 / 32 | |
8DY = 5T! | 8EB = 5U! | 8EB = 5W! | 8EC = 5U! | |
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20 / 32 | 20 / 32 | 20 / 32 | 20 / 32 | |
8EC = 5Z! | 8ED = 5U! | 8EF = 5U! | ||
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40 / 64 | 40 / 64 | 20 / 32 | ||
8EF = 5Z! | 8EM = 5V! | 8EM = 5Z! | ||
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20 / 32 | 20 / 32 | 40 / 64 | ||
8EN = 5N! | 8EP = 5I! | |||
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40 / 64 | 20 / 32 | |||
8EQ = 5W! | 8ES = 5W! | 8ET = 5Z! | 8EW = 5W! | |
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60 / 96 | 20 / 32 | 20 / 32 | 30 / 48 | |
8FA = 5U! | 8FA = 5W! | 8FC = 5Z! | 8FD = 5V! | |
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20 / 32 | 40 / 64 | 20 / 32 | 20 / 32 | |
8FD = 5Z! | 8FE = 5F! | 8FE = 5N! | ||
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20 / 32 | 40 / 64 | 30 / 48 | ||
8FH = 5T! | 8FK = 5I! | 8FK = 5Z! | 8FM = 5U! | |
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20 / 32 | 10 / 16 | 20 / 32 | 20 / 32 | |
8FS = 5V! | 8FT = 5I! | 8FT = 5U! | 8FV = 5V! | |
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20 / 32 | 20 / 32 | 40 / 64 | 20 / 32 | |
8FZ = 5F! | 8FZ = 5I! | 8GA = 5X! | 8GD = 5T! | |
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20 / 32 | 20 / 32 | 20 / 32 | 40 / 64 | |
8GD = 5V! | 8GF = 5U! | 8GG = 5W! | ||
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20 / 32 | 160 / 256 | 40 / 64 | ||
8GJ = 5T! | 8GK = 5T! | 8GN = 5V! | 8GO = 5U! | |
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40 / 64 | 20 / 32 | 40 / 64 | 20 / 32 | |
8GR = 5W! | 8GS = 5U! | 8GX = 5T! | 8GX = 5U! | |
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60 / 96 | 40 / 64 | 20 / 32 | 20 / 32 | |
8GX = 5W! | 8HC = 5U! | 8HF = 5V! | ||
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40 / 64 | 20 / 32 | 20 / 32 | ||
8HH = 5T! | 8HH = 5U! | 8HH = 5Z! | ||
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20 / 32 | 30 / 48 | 40 / 64 | ||
8HK = 5Z! | 8HL = 5Z! | 8HN = 5W! | 8HO = 5U! | |
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20 / 32 | 20 / 32 | 20 / 32 | 20 / 32 | |
8HO = 5W! | 8HO = 5Z! | 8HQ = 5T! | 8HQ = 5Z! | |
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40 / 64 | 20 / 32 | 20 / 32 | 20 / 32 | |
8HT = 5V! | 8HV = 5T! | 8HW = 5T! | 8HX = 5T! | |
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20 / 32 | 20 / 32 | 20 / 32 | 20 / 32 | |
8HY = 5T! | 8HZ = 5V! | 8HZ = 5Z! | 8IA = 5T! | |
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60 / 96 | 20 / 32 | 20 / 32 | 20 / 32 | |
8IB = 5W! | 8IB = 5Z! | 8IC = 5T! | 8II = 5I! | |
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20 / 32 | 40 / 64 | 20 / 32 | 20 / 32 | |
8II = 5Z! | 8IK = 5T! | 8IK = 5Z! | 8IL = 5Z! | |
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20 / 32 | 30 / 48 | 20 / 32 | 40 / 64 | |
8IO = 5W! | 8IT = 5U! | 8IW = 5W! | 8IY = 5T! | |
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20 / 32 | 20 / 32 | 80 / 128 | 20 / 32 | |
8JA = 5U! | 8JA = 5Z! | 8JC = 5T! | ||
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40 / 64 | 20 / 32 | 40 / 64 | ||
8JE = 5W! | 8JH = 5W! | 8JI = 5U! | 8JJ = 5T! | 8JL = 5F! |
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20 / 32 | 20 / 32 | 20 / 32 | 20 / 32 | 20 / 32 |
8JO = 5T! | 8JQ = 5W! | 8JS = 5Z! | 8JT = 5W! | 8JU = 5Z! |
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40 / 64 | 40 / 64 | 30 / 48 | 40 / 64 | 20 / 32 |
8JW = 5L! | 8JX = 5V! | 8JX = 5Z! | 8JZ = 5T! | 8KA = 5F! |
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50 / 80 | 20 / 32 | 20 / 32 | 20 / 32 | 20 / 32 |
8KB = 5T! | 8KD = 5N! | 8KE = 5U! | 8KF = 5X! | |
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40 / 64 | 40 / 64 | 20 / 32 | 20 / 32 | |
8KG = 5T! | 8KG = 5U! | 8KH = 5T! | 8KI = 5Z! | 8KK = 5V! |
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20 / 32 | 20 / 32 | 20 / 32 | 20 / 32 | 20 / 32 |
8KK = 5W! | 8KO = 5V! | 8KO = 5Z! | 8KP = 5Z! | |
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40 / 64 | 20 / 32 | 20 / 32 | 20 / 32 | |
8KS = 5T! | 8KS = 5Z! | 8KT = 5Z! | 8KX = 5I! | |
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20 / 32 | 40 / 64 | 20 / 32 | 60 / 96 | |
8KX = 5T! | 8KZ = 5V! | 8LA = 5V! | 8LB = 5Z! | 8LC = 5T! |
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20 / 32 | 20 / 32 | 20 / 32 | 40 / 64 | 20 / 32 |
8LE = 5U! | 8LE = 5W! | 8LF = 5W! | 8LG = 5W! | |
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20 / 32 | 30 / 48 | 40 / 64 | 20 / 32 | |
8LK = 5U! | 8LK = 5V! | 8LL = 5I! | 8LM = 5Y! | |
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20 / 32 | 20 / 32 | 20 / 32 | 80 / 128 | |
8LN = 5Z! | 8LO = 5T! | 8LP = 5W! | 8LP = 5Z! | |
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20 / 32 | 40 / 64 | 20 / 32 | 10 / 16 | |
8LQ = 5W! | 8LS = 5W! | 8LU = 5W! | ||
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20 / 32 | 80 / 128 | 60 / 96 | ||
8LV = 5U! | 8LW = 5W! | 8LX = 5U! | 8LX = 5Z! | |
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20 / 32 | 20 / 32 | 40 / 64 | 20 / 32 | |
8LY = 5U! | 8LZ = 5F! | 8MC = 5T! | 8MC = 5U! | 8MC = 5Z! |
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20 / 32 | 20 / 32 | 20 / 32 | 20 / 32 | 40 / 64 |
8MD = 5U! | 8MD = 5V! | 8ME = 5U! | ||
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20 / 32 | 60 / 96 | 20 / 32 | ||
8MF = 5N! | 8MI = 5U! | |||
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80 / 128 | 40 / 64 | |||
8MJ = 5I! | 8MJ = 5T! | 8MJ = 5U! | ||
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40 / 64 | 30 / 48 | 20 / 32 | ||
8MK = 5U! | 8MM = 5T! | 8MQ = 5T! | 8MS = 5U! | |
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40 / 64 | 20 / 32 | 10 / 16 | 20 / 32 | |
8MT = 5Y! | 8MW = 5T! | 8MZ = 5U! | ||
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80 / 128 | 20 / 32 | 20 / 32 | ||
8ND = 5Z! | 8NE = 5U! | 8NF = 5Y! | 8NG = 5V! | |
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20 / 32 | 40 / 64 | 20 / 32 | 20 / 32 | |
8NI = 5I! | 8NJ = 5I! | 8NJ = 5U! | ||
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20 / 32 | 40 / 64 | 40 / 64 | ||
8NJ = 5Z! | 8NP = 5Y! | |||
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220 / 352 | 20 / 32 | |||
8NQ = 5U! | 8NQ = 5W! | 8NR = 5L! | ||
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20 / 32 | 20 / 32 | 40 / 64 | ||
8NR = 5Z! | 8NS = 5Z! | 8NT = 5V! | ||
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40 / 64 | 30 / 48 | 20 / 32 | ||
8NU = 5T! | 8NU = 5Z! | 8NW = 5V! | ||
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40 / 64 | 20 / 32 | 20 / 32 | ||
8NX = 5W! | 8NY = 5V! | 8OA = 5N! | 8OB = 5T! | |
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40 / 64 | 20 / 32 | 20 / 32 | 20 / 32 | |
8OC = 5T! | ||||
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20 / 32 |
9ABB = 4I! | 9ADJ = 4I! | 9AIM = 4I | 9AJP = 4I! |
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16 / 36 | 32 / 72 | 16 / 36 | 32 / 72 |
9ATU = 4I! | 9AWZ = 4I! | 9AXB = 4I! | 9AXX = 4I! |
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32 / 72 | 16 / 36 | 16 / 36 | 16 / 36 |
9BAY = 4I! | 9BFG = 4I! | 9BFS = 4I! | 9BGZ = 4I |
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16 / 36 | 16 / 36 | 16 / 36 | 16 / 36 |
9BJX = 4I! | 9BKZ = 4I! | 9BLB = 4I! | 9BLW = 4I! |
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16 / 36 | 16 / 36 | 16 / 36 | 16 / 36 |
9BMS = 4I! | 9BMW = 4I! | 9BNV = 4I! | |
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16 / 36 | 32 / 72 | 16 / 36 |
9ABM = 4Q | 9AJS = 4Q! | 9AOF = 4Q |
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24 / 54 | 32 / 72 | 24 / 54 |
9AYP = 4Q | 9BAR = 4Q! | 9BXI = 4Q! |
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16 / 36 | 32 / 72 | 16 / 36 |
10HKT = 4L |
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16 / 40 |
Last revised 2015-07-15.