POLYOMINO TILINGS

Polyomino Tilings

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


P2 heptomino

Area: 7.

Size: 2x5.

Holes: 0.

Order: 76.

Odd order: ≤ 153.

Prime rectangles: ≥ 26.

Smallest rectangle tilings

Smallest rectangle (19x28):

Smallest known odd rectangle (21x51):

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 \ h1-121314-171819202122-2324252627N>0
1-120
1300
14-170000
180000
19000000
2000000000
21000000000000
22-2300000000000
240000000000000
25000000000000000
260000000022P000??00
270000000000000????00
280000004848P00000?????????
2900000000000????????x
3000000000000?????????
3100000000000?????????
320000000088P0?????????
3300000000000?????????
3400000000000?????????
35000022P00????0?????????
36000000????0?????????
37000000????0?????????
38000000????0?????????
39000000????0?????????
40000000????0?????????
41000000????0?????????
42000088P24382438P????0?????????
43000000????0?????????
44000000????0?????????
45000000????0?????????
46000000????0?????????
47000000????0?????????
48000000????0?????????
4900002020P??????0?????????
500000??????0?????????
510000????≥1≥1P0?????????
520000????≥1≥1C0?????????
530000??????0?????????
540000??????0?????????
550000??????0?????????
5600004040P??????0?????????
570000??????0?????????
580000??????0?????????
590000??????0?????????
600000??????0?????????
610000??????0?????????
620000??????0?????????
630000≥1≥1P??????0?????????
640000??????0?????????
650000??????0?????????
660000??????0?????????
670000??????0?????????
680000??????0?????????
690000??????0?????????
700000≥1≥1C??????0?????????
710000??????0?????????
720000??????0?????????
730000??????0?????????
740000??????0?????????
750000??????0?????????
760000??????0?????????
770000≥1≥1C????≥1≥1C0?????????
780000????≥1≥1C0?????????
790000??????0?????????
800000??????0?????????
810000??????0?????????
820000??????0?????????
830000??????0?????????
840000≥1≥1C??????0?????????
850000??????0?????????
860000??????0?????????
870000??????0?????????
880000??????0?????????
890000??????0?????????
900000??????0?????????
910000≥1≥1C??????0?????????
920000??????0?????????
930000??????0?????????
940000??????0?????????
950000??????0?????????
960000??????0?????????
970000??????0?????????
980000≥1≥1C??????0?????????
990000??????0?????????
1000000??????0?????????
1010000??????0?????????
1020000????≥1≥1C0?????????
1030000????≥1≥1C0?????????
1040000????≥1≥1C0?????????
1050000≥1≥1C??????0?????????
1060000??????0?????????
1070000??????0?????????
1080000??????0?????????
1090000??????0?????????
1100000??????0?????????
1110000??????0?????????
11201818P0≥1≥1C??????0?????????
1130000??????0?????????
1140000??????0?????????
1150000??????0?????????
1160000??????0?????????
1170000??????0?????????
1180000??????0?????????
1190000≥1≥1C??????0?????????
1200000??????0?????????
1210000??????0?????????
1220000??????0?????????
1230000??????0?????????
1240000??????0?????????
1250000??????0?????????
1260228228P0≥1≥1C??????0?????????
1270000??????0?????????
1280000??????0?????????
1290000??????0?????????
1300000??????0?????????
1310000??????0?????????
1320000??????0?????????
1330000≥1≥1C??????0?????????
1340000??????0?????????
1350000??????0?????????
1360000??????0?????????
1370000??????0?????????
1380000??????0?????????
1390000??????0?????????
140012921292P0≥1≥1C??????0?????????
1410000??????0?????????
1420000??????0?????????
1430000??????0?????????
1440000??????0?????????
1450000??????0?????????
1460000??????0?????????
1470432432P0≥1≥1C??????0?????????
1480000??????0?????????
1490000??????0?????????
1500000??????0?????????
1510000??????0?????????
1520000??????0?????????
1530000??????0?????????
154062446244P0≥1≥1C??????0?????????
1550000??????0?????????
1560000??????0?????????
1570000??????0?????????
1580000??????0?????????
1590000??????0?????????
1600000??????0?????????
161049684968P0≥1≥1C??????0?????????
1620000??????0?????????
1630000??????0?????????
1640000??????0?????????
1650000??????0?????????
1660000??????0?????????
1670000??????0?????????
16802931629316P0≥1≥1C??????0?????????
1690000??????0?????????
1700000??????0?????????
1710000??????0?????????
1720000??????0?????????
1730000??????0?????????
1740000??????0?????????
17502440824408P0≥1≥1C??????0?????????
1760000??????0?????????
1770000??????0?????????
1780000??????0?????????
1790000??????0?????????
1800000??????0?????????
1810000??????0?????????
1820100546100546P0≥1≥1C??????0?????????
1830000??????0?????????
1840000??????0?????????
1850000??????0?????????
1860000??????0?????????
1870000??????0?????????
1880000??????0?????????
18908677686776P0≥1≥1C??????0?????????
1900000??????0?????????
1910000??????0?????????
1920000??????0?????????
1930000??????0?????????
1940000??????0?????????
1950000??????0?????????
1960302260302260P0≥1≥1C??????0?????????
1970000??????0?????????
1980000??????0?????????
1990000??????0?????????
2000000??????0?????????
2010000??????0?????????
2020000??????0?????????
2030259828259828P0≥1≥1C??????0?????????
2040000??????0?????????
2050000??????0?????????
2060000??????0?????????
2070000??????0?????????
2080000??????0?????????
2090000??????0?????????
210010725041072504P0≥1≥1C??????0?????????
2110000??????0?????????
2120000??????0?????????
2130000??????0?????????
2140000??????0?????????
2150000??????0?????????
2160000??????0?????????
2170811292811292P0≥1≥1C??????0?????????
2180000??????0?????????
2190000??????0?????????
2200000??????0?????????
2210000??????0?????????
2220000??????0?????????
2230000??????0?????????
224038103383810338C0≥1≥1C??????0?????????
2250000??????0?????????
2260000??????0?????????
2270000??????0?????????
2280000??????0?????????
2290000??????0?????????
2300000??????0?????????
231028874962887496P0≥1≥1C??????0?????????
2320000??????0?????????
2330000??????0?????????
2340000??????0?????????
2350000??????0?????????
2360000??????0?????????
2370000??????0?????????
23801287998812879988C0≥1≥1C??????0?????????
2390000??????0?????????
2400000??????0?????????
2410000??????0?????????
2420000??????0?????????
2430000??????0?????????
2440000??????0?????????
24501047692810476928P0≥1≥1C??????0?????????
2460000??????0?????????
2470000??????0?????????
2480000??????0?????????
2490000??????0?????????
2500000??????0?????????
2510000??????0?????????
25204646502446465024C0≥1≥1C??????0?????????
N>0x7kx7k???x????

Reptile tilings' solutions count (including symmetric)

polyomino \ n²10²11²
P2 heptomino≥10000000000

Attributions

  1. Rectangle 21x51 taken from http://www.cflmath.com/~reid/Polyomino/7omino5_rect.html

See Also

P1 heptominoP3 heptomino