POLYOMINO TILINGS

Polyomino Tilings

Select polyominoes for a set (currently 1 or 2), for which tilings should be shown.

Then click "Show" button.

You may also see list of all polyomino sets for which data is available here.


T1 hexomino and I1 octomino

Prime rectangles: ≥ 28.

Smallest rectangle tilings

Smallest known rectangle (9x48):

Rectangle tilings' solutions count (including symmetric)

Blue number (P) - strongly prime rectangle (which cannot be divided into two or more number of rectangles tileable by this set).

Green number (W) - weakly prime rectangle (which cannot be divided into two rectangles tileable by this set, but which can be divided into three or more rectangles).

Red number (C) - composite rectangle (which can be divided into two rectangles tileable by this set).

Gray number - it is unknown whether rectangle is prime or composite.

Question mark (?) - solution count is unknown.

Click on underlined numbers to view picture with one solution.

w \ h1-89101112131415161718N>0
1-80
9000
1000000
110000000
12000000000
13000000000??
14000000000????
15000000000??????
16000000000????????
17000000000??????????
18000000000????????????
19000000000?????????????
20000000000?????????????
21000000000?????????????
22000000000?????????????
23000000000?????????????
24000000000?????????????
25000000000?????????????
26000000000?????????????
27000000000?????????????
28000000000?????????????
29000000000?????????????
30000000000?????????????
31000000000?????????????
32000000000?????????????
33000000000?????????????
34000000000?????????????
35000000000?????????????
36000000000?????????????
37000000000?????????????
38000000000?????????????
39000000000?????????????
400000022P44?????????????
41000000000?????????????
42000000000?????????????
43000000000?????????????
44000000000?????????????
45000000000?????????????
46000000000?????????????
47000000000?????????????
48022P55P102102P245245?????????????
49000000000?????????????
50000000000?????????????
51000000000?????????????
52000000000?????????????
53000000000?????????????
54000000000?????????????
55000000000?????????????
5605858P427427P32723272P1318913189?????????????
57000000000?????????????
58000000000?????????????
59000000000?????????????
60000000000?????????????
61000000000?????????????
62000000000?????????????
63000000000?????????????
640938938P2981429814P109256109256P716260716260?????????????
65000000000?????????????
66000000000?????????????
67000000000?????????????
68000000000?????????????
69000000000?????????????
70000000000?????????????
71000000000?????????????
7201138611386P13443541344354P36512363651236P3349178633491786?????????????
73000000000?????????????
74000000000?????????????
75000000000?????????????
760000022P00?????????????
77000000000?????????????
78000000000?????????????
79000000000?????????????
800117338117338P4120257741202577P102508534102508534C1.47114400×10¹⁰1471144001?????????????
81000000000?????????????
82000000000?????????????
83000000000?????????????
8400000100100P00?????????????
85000000000?????????????
86000000000?????????????
87000000000?????????????
88010961961096196P940694603940694603P2.32701780×10¹⁰2327017804C6.52310994×10¹¹65231099497?????????????
89000000000?????????????
90000000000?????????????
91000000000?????????????
920000026922692P00?????????????
93000000000?????????????
94000000000?????????????
95000000000?????????????
96096423069642306C1.71889245×10¹¹17188924589C4.39074249×10¹¹43907424960C2.71780478×10¹³2717804781817?????????????
97000000000?????????????
98000000000?????????????
99000000000?????????????
100000005247852478P00?????????????
101000000000?????????????
102000000000?????????????
103000000000?????????????
10408163978081639780C2.65277908×10¹²265277908670C7.15896129×10¹²715896129718C9.84514367×10¹⁴98451436761000?????????????
105000000000?????????????
106000000000?????????????
107000000000?????????????
10800000839296839296P00?????????????
109000000000?????????????
110000000000?????????????
111000000000?????????????
1120673640462673640462C3.60565912×10¹³3605659121634C1.04514220×10¹⁴10451422066284C3.04434994×10¹⁶3044349947882028?????????????
113000000000?????????????
114000000000?????????????
115000000000?????????????
116000001180218411802184C00?????????????
117000000013521352?????????????
118000000000?????????????
119000000000?????????????
12005.45298811×10¹⁰5452988114C4.46451492×10¹⁴44645149241670C1.40720401×10¹⁵140720401847262C8.17006211×10¹⁷81700621198690560?????????????
121000000000?????????????
122000000000?????????????
123000000000?????????????
12400000152342308152342308C00?????????????
125000000011790481179048?????????????
126000000000?????????????
127000000000?????????????
12804.34576711×10¹¹43457671186C5.17832365×10¹⁵517832365847283C1.78923050×10¹⁶1789230501554802C1.95725865×10¹⁹1957258652761029494?????????????
129000000000?????????????
130000000000?????????????
131000000000?????????????
132000001.85823625×10¹⁰1858236252C00?????????????
1330000000417757680417757680?????????????
134000000000?????????????
135000000000?????????????
13603.41725413×10¹²341725413760C5.76074590×10¹⁶5760745908722648C2.18891968×10¹⁷21889196843440590C???????????????
137000000000?????????????
138000000000?????????????
139000000000?????????????
140000002.19181026×10¹¹21918102608C4743247432?????????????
14100000008.16369703×10¹¹81636970330?????????????
142000000000?????????????
143000000000?????????????
14402.65585881×10¹³2655858816538C6.27906971×10¹⁷62790697179271459C2.61667321×10¹⁸261667321191369738C???????????????
145000000000?????????????
146000000044?????????????
147000000000?????????????
148000002.56095102×10¹²256095102512C4586696845866968?????????????
14900000001.03606911×10¹⁴10360691116362?????????????
150000000000?????????????
15100000001010?????????????
15202.04319601×10¹⁴20431960103544C6.84907246×10¹⁸684907246723340519C3.09900856×10¹⁹3099008560217631274C???????????????
153000000000?????????????
1540000000546546?????????????
155000000000?????????????
156000003.06687046×10¹³3066870465072C1.94961941×10¹¹19496194134?????????????
15700000009.42616105×10¹⁵942616105239644?????????????
158000000000?????????????
159000000016561656?????????????
16001.55810516×10¹⁵155810516302326C7.63303733×10¹⁹7633037333749486810C≥1≥1C???????????????
1610000000240240?????????????
16200000004555845558?????????????
163000000000?????????????
164000004.02314875×10¹⁴40231487551406C4.99800010×10¹³4998000106938?????????????
16500000006.56322764×10¹⁷65632276475549230?????????????
166000000012341234?????????????
1670000000146578146578?????????????
16801.17923410×10¹⁶1179234108229234C≥1≥1C≥1≥1C???????????????
16900000004582845828?????????????
170000000031072143107214?????????????
171000000052725272?????????????
172000006.58195018×10¹⁵658195018586732C8.81426644×10¹⁵881426644692848?????????????
17300000003.66350358×10¹⁹3663503580818633314?????????????
1740000000247564247564?????????????
175000000096546009654600?????????????
17608.86696229×10¹⁶8866962292567138C≥1≥1C≥1≥1C???????????????
177000000047308864730886?????????????
1780000000186219048186219048?????????????
179000000011621641162164?????????????
1800001818P1.48278658×10¹⁷14827865840780260C1.15161467×10¹⁸115161467400982510?????????????
1810000000???????????????
18200000002726244827262448?????????????
1830000000540297042540297042?????????????
18406.62976764×10¹⁷66297676425690072C≥1≥1C≥1≥1C???????????????
1850??0000358035816358035816?????????????
1860??00001.00173180×10¹¹10017318052?????????????
1870??0000138056452138056452?????????????
1880??24842484P4.12228506×10¹⁸412228506265794920C1.17071216×10²⁰11707121670577815428?????????????
1890??0000???????????????
1900??00002.20247862×10¹⁰2202478620?????????????
1910??00002.71185922×10¹¹27118592282?????????????
1920??≥1≥1C≥1≥1C???????????????
1930??00002.24615292×10¹¹22461529210?????????????
1940??00004.89189983×10¹²489189983778?????????????
1950??00001.18583605×10¹¹11858360544?????????????
1960??234738234738P1.17809081×10²⁰11780908175360542434C???????????????
1970??0000???????????????
1980??00001.46411645×10¹²146411645162?????????????
1990??00001.25432035×10¹³1254320359894?????????????
2000??≥1≥1C≥1≥1C???????????????
2010?????????????????????
2020?????????????????????
2030?????????????????????
2040??≥1≥1P?????????????????
2050?????????????????????
2060?????????????????????
2070?????????????????????
2080??≥1≥1C?????????????????
2090?????????????????????
2100?????????????????????
2110?????????????????????
2120??≥1≥1P?????????????????
2130?????????????????????
2140?????????????????????
2150?????????????????????
2160??≥1≥1C?????????????????
2170?????????????????????
2180?????????????????????
2190?????????????????????
2200??≥1≥1P?????????????????
2210?????????????????????
2220?????????????????????
2230?????????????????????
2240??≥1≥1C?????????????????
2250?????????????????????
2260?????????????????????
2270?????????????????????
2280??≥1≥1C?????????????????
N>0x??????????

Attributions

  1. Smallest rectangle have been found by Florian Fischer

See Also

T1 hexomino and I heptominoT1 hexomino and I 9-omino