Addendum to Polypolyominoes

Introduction

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!

Solutions

HAGINOYA Ichiji (萩野谷一二) deepgreen improved on a pentomino-tetromino solution that I derived from a construction by Helmut POSTL.

Edo TIMMERMANS improved on one of my hexomino-pentomino solutions. I later improved on his.

Pentominoes and Tetrominoes

5T = 4Q
68 / 85

Hexominoes and Pentominoes

6AC = 5Y	6AE = 5U	6BG = 5X!	6BH = 5Z
5 / 6	40 / 48	80 / 96	40 / 48

Hexominoes and Hexominoes

6AX = 6AZ!
68 / 68

Heptominoes and Tetrominoes

7BX = 4Q	7CY = 4N	7DY = 4T!	7EB = 4Q
16 / 28	32 / 56	32 / 56	32 / 56
7CU = 4Q!
128 / 224

Heptominoes and Pentominoes FILN

7AP = 5N!	7AV = 5L!	7AY = 5I	7BN = 5I
70 / 98	40 / 56	20 / 28	30 / 42

Heptominoes and Pentominoes PTUV

7AI = 5U	7AV = 5P!	7AY = 5U	7BL = 5T
30 / 42	40 / 56	30 / 42	30 / 42
7CD = 5U	7CW = 5V	7CX = 5V	7DA = 5V
30 / 42	30 / 42	20 / 28	20 / 28
7DF = 5T	7DG = 5T	7DN = 5T!	7DO = 5V
30 / 42	30 / 42	40 / 56	30 / 42
7DR = 5T	7DW = 5U	7DX = 5T
30 / 42	20 / 28	30 / 42

Heptominoes and Pentominoes WXYZ

7AN = 5Z	7AT = 5Z	7BL = 5Z	7CB = 5Z
30 / 42	20 / 28	30 / 42	20 / 28
7CH = 5W	7CJ = 5Z	7CQ = 5X!
30 / 42	30 / 42	100 / 140
7CV = 5Z	7DE = 5Z!	7DL = 5Y	7DQ = 5Z!
30 / 42	40 / 56	20 / 28	50 / 70

Octominoes and Tromino I

8KD = 3I	8MY = 3I!
24 / 64	66 / 176

Octominoes and Tetromino I

8DP = 4I
28 / 56

Octominoes and Tetromino N

8LZ = 4N!
48 / 96

Octominoes and Tetromino Q

8BV = 4Q!	8DM = 4Q!	8JA = 4Q!
56 / 112	52 / 104	44 / 88
8KQ = 4Q!	8MO = 4Q	8MP = 4Q
28 / 56	28 / 56	24 / 48

Octominoes and Pentominoes

8AF = 5F!		8AF = 5V!	8AI = 5Z!	8AK = 5T!
60 / 96		20 / 32	20 / 32	20 / 32
8AL = 5T!	8AN = 5T!		8AN = 5W!	8AN = 5Z!
20 / 32	40 / 64		20 / 32	20 / 32
8AQ = 5T!		8AQ = 5V!	8AR = 5T!
40 / 64		20 / 32	20 / 32
8AZ = 5L!		8AZ = 5Z!	8BD = 5P!
20 / 32		20 / 32	20 / 32
8BD = 5Z!		8BF = 5V!	8BH = 5V!	8BQ = 5V!
20 / 32		20 / 32	20 / 32	20 / 32
8BR = 5T!	8BR = 5V!	8BX = 5V!	8BZ = 5U!	8CA = 5Z!
20 / 32	20 / 32	20 / 32	20 / 32	20 / 32
8CB = 5T!	8CD = 5I!		8CE = 5W!	8CH = 5T!
40 / 64	40 / 64		20 / 32	20 / 32
8CI = 5V!	8CJ = 5T!	8CK = 5T!	8CN = 5Z!	8CO = 5T!
20 / 32	20 / 32	20 / 32	20 / 32	20 / 32
8CR = 5W!		8CU = 5U!		8CU = 5V!
40 / 64		40 / 64		20 / 32
8CU = 5W!		8CW = 5Z!	8CZ = 5T!
40 / 64		20 / 32	20 / 32
8DA = 5W!		8DE = 5N!	8DF = 5Z!	8DG = 5U!
40 / 64		10 / 16	20 / 32	20 / 32
8DH = 5U!	8DI = 5V!		8DL = 5U!	8DM = 5V!
20 / 32	40 / 64		20 / 32	40 / 64
8DO = 5T!		8DO = 5U!	8DQ = 5U!
40 / 64		20 / 32	40 / 64
8DR = 5T!		8DU = 5U!	8DV = 5V!	8DX = 5Z!
40 / 64		20 / 32	20 / 32	20 / 32
8DY = 5T!	8EB = 5U!	8EB = 5W!	8EC = 5U!
20 / 32	20 / 32	20 / 32	20 / 32
8EC = 5Z!		8ED = 5U!		8EF = 5U!
40 / 64		40 / 64		20 / 32
8EF = 5Z!	8EM = 5V!	8EM = 5Z!
20 / 32	20 / 32	40 / 64
8EN = 5N!		8EP = 5I!
40 / 64		20 / 32
8EQ = 5W!		8ES = 5W!	8ET = 5Z!	8EW = 5W!
60 / 96		20 / 32	20 / 32	30 / 48
8FA = 5U!	8FA = 5W!		8FC = 5Z!	8FD = 5V!
20 / 32	40 / 64		20 / 32	20 / 32
8FD = 5Z!	8FE = 5F!		8FE = 5N!
20 / 32	40 / 64		30 / 48
8FH = 5T!		8FK = 5I!	8FK = 5Z!	8FM = 5U!
20 / 32		10 / 16	20 / 32	20 / 32
8FS = 5V!	8FT = 5I!	8FT = 5U!		8FV = 5V!
20 / 32	20 / 32	40 / 64		20 / 32
8FZ = 5F!	8FZ = 5I!	8GA = 5X!	8GD = 5T!
20 / 32	20 / 32	20 / 32	40 / 64
8GD = 5V!	8GF = 5U!			8GG = 5W!
20 / 32	160 / 256			40 / 64
8GJ = 5T!	8GK = 5T!	8GN = 5V!		8GO = 5U!
40 / 64	20 / 32	40 / 64		20 / 32
8GR = 5W!	8GS = 5U!		8GX = 5T!	8GX = 5U!
60 / 96	40 / 64		20 / 32	20 / 32
8GX = 5W!		8HC = 5U!	8HF = 5V!
40 / 64		20 / 32	20 / 32
8HH = 5T!		8HH = 5U!	8HH = 5Z!
20 / 32		30 / 48	40 / 64
8HK = 5Z!	8HL = 5Z!	8HN = 5W!	8HO = 5U!
20 / 32	20 / 32	20 / 32	20 / 32
8HO = 5W!		8HO = 5Z!	8HQ = 5T!	8HQ = 5Z!
40 / 64		20 / 32	20 / 32	20 / 32
8HT = 5V!	8HV = 5T!	8HW = 5T!	8HX = 5T!
20 / 32	20 / 32	20 / 32	20 / 32
8HY = 5T!		8HZ = 5V!	8HZ = 5Z!	8IA = 5T!
60 / 96		20 / 32	20 / 32	20 / 32
8IB = 5W!	8IB = 5Z!		8IC = 5T!	8II = 5I!
20 / 32	40 / 64		20 / 32	20 / 32
8II = 5Z!	8IK = 5T!	8IK = 5Z!	8IL = 5Z!
20 / 32	30 / 48	20 / 32	40 / 64
8IO = 5W!	8IT = 5U!	8IW = 5W!		8IY = 5T!
20 / 32	20 / 32	80 / 128		20 / 32
8JA = 5U!		8JA = 5Z!	8JC = 5T!
40 / 64		20 / 32	40 / 64
8JE = 5W!	8JH = 5W!	8JI = 5U!	8JJ = 5T!	8JL = 5F!
20 / 32	20 / 32	20 / 32	20 / 32	20 / 32
8JO = 5T!	8JQ = 5W!	8JS = 5Z!	8JT = 5W!	8JU = 5Z!
40 / 64	40 / 64	30 / 48	40 / 64	20 / 32
8JW = 5L!	8JX = 5V!	8JX = 5Z!	8JZ = 5T!	8KA = 5F!
50 / 80	20 / 32	20 / 32	20 / 32	20 / 32
8KB = 5T!		8KD = 5N!	8KE = 5U!	8KF = 5X!
40 / 64		40 / 64	20 / 32	20 / 32
8KG = 5T!	8KG = 5U!	8KH = 5T!	8KI = 5Z!	8KK = 5V!
20 / 32	20 / 32	20 / 32	20 / 32	20 / 32
8KK = 5W!		8KO = 5V!	8KO = 5Z!	8KP = 5Z!
40 / 64		20 / 32	20 / 32	20 / 32
8KS = 5T!	8KS = 5Z!	8KT = 5Z!	8KX = 5I!
20 / 32	40 / 64	20 / 32	60 / 96
8KX = 5T!	8KZ = 5V!	8LA = 5V!	8LB = 5Z!	8LC = 5T!
20 / 32	20 / 32	20 / 32	40 / 64	20 / 32
8LE = 5U!	8LE = 5W!	8LF = 5W!		8LG = 5W!
20 / 32	30 / 48	40 / 64		20 / 32
8LK = 5U!	8LK = 5V!	8LL = 5I!	8LM = 5Y!
20 / 32	20 / 32	20 / 32	80 / 128
8LN = 5Z!	8LO = 5T!		8LP = 5W!	8LP = 5Z!
20 / 32	40 / 64		20 / 32	10 / 16
8LQ = 5W!	8LS = 5W!		8LU = 5W!
20 / 32	80 / 128		60 / 96
8LV = 5U!	8LW = 5W!	8LX = 5U!		8LX = 5Z!
20 / 32	20 / 32	40 / 64		20 / 32
8LY = 5U!	8LZ = 5F!	8MC = 5T!	8MC = 5U!	8MC = 5Z!
20 / 32	20 / 32	20 / 32	20 / 32	40 / 64
8MD = 5U!	8MD = 5V!		8ME = 5U!
20 / 32	60 / 96		20 / 32
8MF = 5N!		8MI = 5U!
80 / 128		40 / 64
8MJ = 5I!		8MJ = 5T!	8MJ = 5U!
40 / 64		30 / 48	20 / 32
8MK = 5U!		8MM = 5T!	8MQ = 5T!	8MS = 5U!
40 / 64		20 / 32	10 / 16	20 / 32
8MT = 5Y!			8MW = 5T!	8MZ = 5U!
80 / 128			20 / 32	20 / 32
8ND = 5Z!	8NE = 5U!		8NF = 5Y!	8NG = 5V!
20 / 32	40 / 64		20 / 32	20 / 32
8NI = 5I!	8NJ = 5I!		8NJ = 5U!
20 / 32	40 / 64		40 / 64
8NJ = 5Z!				8NP = 5Y!
220 / 352				20 / 32
8NQ = 5U!	8NQ = 5W!	8NR = 5L!
20 / 32	20 / 32	40 / 64
8NR = 5Z!		8NS = 5Z!	8NT = 5V!
40 / 64		30 / 48	20 / 32
8NU = 5T!		8NU = 5Z!	8NW = 5V!
40 / 64		20 / 32	20 / 32
8NX = 5W!		8NY = 5V!	8OA = 5N!	8OB = 5T!
40 / 64		20 / 32	20 / 32	20 / 32
8OC = 5T!
20 / 32

Enneominoes and Tetromino I

9ABB = 4I!	9ADJ = 4I!	9AIM = 4I	9AJP = 4I!
16 / 36	32 / 72	16 / 36	32 / 72
9ATU = 4I!	9AWZ = 4I!	9AXB = 4I!	9AXX = 4I!
32 / 72	16 / 36	16 / 36	16 / 36
9BAY = 4I!	9BFG = 4I!	9BFS = 4I!	9BGZ = 4I
16 / 36	16 / 36	16 / 36	16 / 36
9BJX = 4I!	9BKZ = 4I!	9BLB = 4I!	9BLW = 4I!
16 / 36	16 / 36	16 / 36	16 / 36
9BMS = 4I!	9BMW = 4I!	9BNV = 4I!
16 / 36	32 / 72	16 / 36

Enneominoes and Tetromino Q

9ABM = 4Q	9AJS = 4Q!	9AOF = 4Q
24 / 54	32 / 72	24 / 54
9AYP = 4Q	9BAR = 4Q!	9BXI = 4Q!
16 / 36	32 / 72	16 / 36

Decominoes and Tetromino L

10HKT = 4L
16 / 40

Last revised 2024-02-02.