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.


T tetromino and Z tetromino

Prime rectangles: 7.

Smallest rectangle tilings

Smallest rectangle (4x5):

Smallest square (8x8):

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 \ h1-3456789101112N>0
1-30
4000
5044P0
6088P000
701818P000
803838P6464C192192C16481648C2099420994C
90104104P000108836108836C0
100242242C0000574394574394C019486481948648P
110564564C00038287983828798C000
12013021302C12161216C50005000C261558261558C2713951227139512C202910308202910308C2.14734763×10¹⁰2147347636C5.36061914×10¹¹53606191458C1.56032340×10¹³1560323400636C
13030903090C000171246674171246674C0002.28369656×10¹⁴22836965631394C?
14072287228C0928928P01.05537535×10¹⁰1055375354C03.05809863×10¹¹30580986328C03.47914510×10¹⁵347914510514730C?
1501690416904C0006.78662211×10¹⁰6786622118C0006.97913846×10¹⁶6979138468109468C?
1603948439484C2414824148C134960134960C5481167454811674C4.41874118×10¹¹44187411810C4.58733621×10¹²458733621670C9.42922154×10¹³9429221547880C1.07323205×10¹⁶1073232058878602C1.45806283×10¹⁸145806283122424876C?
1709248492484C0002.83449698×10¹²283449698088C0002.55228372×10¹⁹2552283729790394556C?
180216328216328C06051260512C01.80491985×10¹³1804919855716C02.68407271×10¹⁵268407271991556C0≥1.84467440×10²⁰≥18446744073709551615C?
190506002506002C0001.15698106×10¹⁴11569810625218C000≥1.84467440×10²⁰≥18446744073709551615C?
20011834021183402C484632484632C37129203712920C1.27308601×10¹¹12730860118C7.43625907×10¹⁴74362590776908C1.12341220×10¹⁶1123412204609906C4.54321320×10¹⁷45432132011048126C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
21027684242768424C0004.77077813×10¹⁵477077813438822C000≥1.84467440×10²⁰≥18446744073709551615C?
22064755066475506C027580482758048C03.05579651×10¹⁶3055796513149026C01.90583773×10¹⁹1905837733293955176C0≥1.84467440×10²⁰≥18446744073709551615C?
2301514658015146580C0001.95914892×10¹⁷19591489238540534C000≥1.84467440×10²⁰≥18446744073709551615C?
2403542822635428226C97578069757806C103288088103288088C3.04985662×10¹³3049856624988C1.25673562×10¹⁸125673562902584584C2.85139648×10¹⁹2851396483283299878C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
2508286977882869778C0008.06006413×10¹⁸806006413571338270C000≥1.84467440×10²⁰≥18446744073709551615C?
N>0xall4k2k4kall4k2k4kall

See Also

O tetromino and Z2 hexominoT tetromino and I pentomino