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.


L tetromino and V pentomino

Prime rectangles: 20.

Smallest rectangle tilings

Smallest rectangle (3x6):

Smallest square (5x5):

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 \ h1-2345678N>0
1-20
3000
400000
5000004848P
6044P002828P7272C
7088P004444P15441544C17681768P
8000002424P10641064C1275012750C116100116100P
90001010P496496P1470814708C198492198492C13965101396510Call
100004040P83348334C4860648606C681014681014C1086820410868204Call
11000156156P58165816C360354360354C71782167178216C105962514105962514C?
1201616C504504P1953819538C878704878704C2901982829019828C785086968785086968C?
1306464C15521552P135704135704C47396204739620C152849340152849340C6.99721099×10¹⁰6997210994C?
140104104C43564356P166528166528C2007367620073676C1.27453420×10¹⁰1274534200C5.29286132×10¹¹52928613228C?
1508080P1204412044P14721201472120C9519067095190670C5.17659788×10¹⁰5176597884C4.45250232×10¹²445250232610C?
160003163431634P15607301560730C350418746350418746C3.21775137×10¹¹32177513778C3.43818851×10¹³3438188518064C?
170008204882048P57390605739060C1.52492730×10¹⁰1524927308C2.25431714×10¹²225431714016C2.80959785×10¹⁴28095978549504C?
1806464C206530206530C3212939432129394C6.62640527×10¹⁰6626405274C1.01002293×10¹³1010022939072C2.20809418×10¹⁵220809418190764C?
190384384C515574515574C4883609648836096C2.88417561×10¹¹28841756112C6.75018634×10¹³6750186347236C1.77984248×10¹⁶1779842481561560C?
20010241024C12617921261792C287524932287524932C1.15296944×10¹²115296944774C4.02146255×10¹⁴40214625500822C1.41298706×10¹⁷14129870646474986C?
21015361536C30720663072066C577612504577612504C4.92673772×10¹²492673772488C2.02099224×10¹⁵202099224807148C1.13102034×10¹⁸113102034218970254C?
22013601360C73811447381144C1.55246792×10¹⁰1552467924C2.08139836×10¹³2081398368298C1.30647595×10¹⁶1306475954938914C9.01031580×10¹⁸901031580381404256C?
230672672P1767630217676302C7.33410798×10¹⁰7334107984C8.98719598×10¹³8987195982170C7.35796431×10¹⁶7357964315851324C7.18725376×10¹⁹7187253768051810368C?
240256256C4195159441951594C1.31135805×10¹¹13113580548C3.65654432×10¹⁴36565443233382C3.99030076×10¹⁷39903007634657758C≥1.84467440×10²⁰≥18446744073709551615C?
25020482048C9937503499375034C6.08586518×10¹¹60858651848C1.55865096×10¹⁵155865096731460C2.48162537×10¹⁸248162537265088932C≥1.84467440×10²⁰≥18446744073709551615C?
N>0xallallallallallall

See Also

L tetromino and U pentominoL tetromino and W pentomino