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.


P1 heptomino

Area: 7.

Size: 2x5.

Holes: 0.

Order: 2.

Square order: 28.

Odd order: ≤ 57.

Prime rectangles: ≥ 4.

Smallest rectangle tilings

Smallest rectangle (2x7):

Smallest square (14x14):

Smallest known odd rectangle (19x21):

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 \ h12345678910111213141516171819N>0
10
200
3000
40000
500000
6000000
7022P044C01010C0
80000003232C0
90000000000
100000008888C0000
11000000000000
12000000228228C000000
1300000000000000
14044C01616C0100100C600600C11521152C48324832C87728772C2972829728C5896858968C213664213664C817344817344C
1500000000000000≥10000≥10000C00
1600000016321632C0000000≥10000≥10000C00??
1700000000000000≥10000≥10000C00????
1800000044244424C0000000≥10000≥10000C00??????
1900000000000000≥10000≥10000C00????????
200000001187211872C0000000≥10000≥10000C00?????????
21088C06464C010001000C04300843008C00895616895616C001560876815608768C00≥10000≥10000C????????≥1≥1P?
220000003180831808C0000000≥1≥1C???????????
2300000000000000≥1≥1C???????????
240000008552085520C0000000≥1≥1C???????????
2500000000000000≥1≥1C???????????
26000000230176230176C0000000≥1≥1C???????????
2700000000000000≥1≥1C???????????
2801616C0256256C01000010000C618944618944C16220161622016C3190220831902208C9183080091830800C1.17074892×10¹⁰1170748928C4.15324598×10¹⁰4153245984C6.05523824×10¹¹60552382464C≥1≥1C???????????
2900000000000000?????????????
3000000016633921663392C0000000?????????????
3100000000000000?????????????
3200000044712964471296C0000000?????????????
3300000000000000?????????????
340000001202188812021888C0000000?????????????
3503232C010241024C0100000100000C06134169661341696C009.42283123×10¹⁰9422831232C001.10679123×10¹³1106791238272C121176064121176064P?????????????
360000003232211232322112C0000000?????????????
3700000000000000?????????????
380000008689395286893952C0000000?????????????
3900000000000000?????????????
40000000233602048233602048C0000000?????????????
4100000000000000?????????????
4206464C040964096C010000001000000C628023424628023424C2.32154726×10¹⁰2321547264C2.09356900×10¹²209356900352C9.67017607×10¹²967017607232C4.80269756×10¹⁴48026975608832C2.95100303×10¹⁵295100303855232C1.79359185×10¹⁷17935918547231744C?????????????
4300000000000000?????????????
440000001.68841164×10¹⁰1688411648C0000000?????????????
4500000000000000?????????????
460000004.53917900×10¹⁰4539179008C0000000?????????????
4700000000000000?????????????
480000001.22032212×10¹¹12203221248C0000000?????????????
490128128C01638416384C01000000010000000C08.78790574×10¹¹87879057408C009.92428569×10¹⁴99242856950784C330301440330301440P7.86967688×10¹⁷78696768833603072C9.71336648×10¹⁴97133664862208C?????????????
500000003.28074531×10¹¹32807453184C0000000?????????????
5100000000000000?????????????
520000008.82005575×10¹¹88200557568C0000000?????????????
5300000000000000?????????????
540000002.37120989×10¹²237120989696C0000000?????????????
5500000000000000?????????????
560256256C06553665536C0100000000100000000C6.37482655×10¹²637482655744C3.32672060×10¹³3326720606208C1.37407602×10¹⁶1374076021121024C1.01851365×10¹⁷10185136554242304C2.03496101×10¹⁹2034961017768869888C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?????????????
N>0x7kx7kx7k2k7k?7k7k7k7k??????

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
P1 heptomino100000

Attributions

  1. Prime rectangles list taken from http://www.cflmath.com/~reid/Polyomino/7omino2_rect.html

See Also

L1 heptominoP2 heptomino