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.


W pentomino and Y2 hexomino

Prime rectangles: ≥ 42.

Smallest rectangle tilings

Smallest rectangle (14x25):

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 \ h1-12131415161718N>0
1-120
13000
1400000
150000000
16000000000
1700000000000
180000000000000
190000000000000?
200000000000000?
210000000000000?
220000000000000?
230000000000000?
2400000000000≥1≥1?
2500022P00000000?
2600000?????????
2700000?????????
2800000?????????
2900000?????????
3000000?????????
3100044P?????????
3200000?????????
3300000?????????
34022P00?????????
3500000?????????
3600044P?????????
37044P22P?????????
3800022P?????????
3900000?????????
4000044P?????????
4100000?????????
4200000?????????
430001010P?????????
440002020P?????????
450005858P?????????
460002424P?????????
47000≥1≥1P?????????
48000≥1≥1P?????????
49000≥1≥1P?????????
50000≥1≥1C?????????
51000≥1≥1?????????
52022P≥1≥1?????????
53000≥1≥1?????????
54066P≥1≥1?????????
55000≥1≥1?????????
56088P≥1≥1?????????
57000≥1≥1?????????
5803232P≥1≥1?????????
59088P≥1≥1?????????
60022P≥1≥1?????????
61000≥1≥1?????????
62000≥1≥1?????????
6304848P≥1≥1?????????
6403030P≥1≥1?????????
6502828P≥1≥1?????????
6607676P≥1≥1?????????
6707272P≥1≥1?????????
6809292C≥1≥1?????????
690140140P≥1≥1?????????
700164164P???????????
710188188C???????????
720254254P???????????
730336336P???????????
740430430C???????????
750508508P???????????
760708708P???????????
770852852P???????????
78012061206P???????????
79019961996P???????????
80022122212P???????????
81025002500P???????????
82034043404P???????????
83043164316P???????????
84053965396P???????????
85070527052P???????????
86094729472C???????????
8701367213672P???????????
8801740417404C???????????
8902185221852C???????????
9003014630146C???????????
9103731237312C???????????
9204994849948C???????????
9306410864108C???????????
9408453084530C???????????
950113776113776C???????????
960145324145324C???????????
970184420184420C???????????
980248300248300C???????????
990314896314896C???????????
1000417472417472C???????????
1010550672550672C???????????
1020713380713380C???????????
1030934284934284C???????????
104012223341222334C???????????
105016087761608776C???????????
106020791962079196C???????????
107027158602715860C???????????
108035513563551356C???????????
109046617324661732C???????????
110061009286100928C???????????
111079761367976136C???????????
11201041019010410190C???????????
11301361744813617448C???????????
11401771580617715806C???????????
11502318152023181520C???????????
11603032436430324364C???????????
11703955792439557924C???????????
11805175683051756830C???????????
11906755570867555708C???????????
12008848079488480794C???????????
1210115500880115500880C???????????
1220150932786150932786C???????????
1230196976512196976512C???????????
1240257950844257950844C???????????
1250336916928336916928C???????????
1260440348576440348576C???????????
1270575181868575181868C???????????
1280752257726752257726C???????????
1290982509400982509400C???????????
13001.28332983×10¹⁰1283329832C???????????
13101.67691066×10¹⁰1676910660C???????????
13202.19142439×10¹⁰2191424394C???????????
13302.86417701×10¹⁰2864177012C???????????
13403.74283282×10¹⁰3742832820C???????????
13504.89094328×10¹⁰4890943284C???????????
13606.39049377×10¹⁰6390493778C???????????
13708.35365228×10¹⁰8353652288C???????????
13801.09148789×10¹¹10914878946C???????????
13901.42625511×10¹¹14262551192C???????????
14001.86388845×10¹¹18638884576C???????????
14102.43549205×10¹¹24354920596C???????????
14203.18251384×10¹¹31825138470C???????????
14304.15953530×10¹¹41595353032C???????????
14405.43445828×10¹¹54344582836C???????????
14507.10247115×10¹¹71024711540C???????????
14609.28123383×10¹¹92812338306C???????????
14701.21276366×10¹²121276366984C???????????
14801.58481366×10¹²158481366048C???????????
14902.07088768×10¹²207088768656C???????????
15002.70618115×10¹²270618115004C???????????
15103.53647556×10¹²353647556016C???????????
15204.62128238×10¹²462128238422C???????????
15306.03914012×10¹²603914012172C???????????
15407.89193122×10¹²789193122650C???????????
15501.03127213×10¹³1031272138772C???????????
15601.34763311×10¹³1347633116326C???????????
15701.76104661×10¹³1761046617596C???????????
15802.30122787×10¹³2301227874970C???????????
15903.00719258×10¹³3007192584400C???????????
16003.92972391×10¹³3929723912136C???????????
16105.13522088×10¹³5135220889616C???????????
16206.71059430×10¹³6710594309310C???????????
16308.76914837×10¹³8769148378684C???????????
16401.14592185×10¹⁴11459218560068C???????????
16501.49743518×10¹⁴14974351863376C???????????
16601.95681650×10¹⁴19568165059382C???????????
16702.55710075×10¹⁴25571007528868C???????????
16803.34154035×10¹⁴33415403555166C???????????
16904.36661603×10¹⁴43666160362624C???????????
17005.70616572×10¹⁴57061657282592C???????????
17107.45663906×10¹⁴74566390696904C???????????
17209.74406265×10¹⁴97440626564514C???????????
17301.27332041×10¹⁵127332041323628C???????????
17401.66393608×10¹⁵166393608881452C???????????
17502.17437175×10¹⁵217437175772252C???????????
17602.84139689×10¹⁵284139689198002C???????????
17703.71304987×10¹⁵371304987940912C???????????
17804.85209368×10¹⁵485209368745736C???????????
17906.34055651×10¹⁵634055651669236C???????????
18008.28562410×10¹⁵828562410009164C???????????
18101.08273775×10¹⁶1082737756731776C???????????
18201.41488663×10¹⁶1414886636571788C???????????
18301.84892492×10¹⁶1848924924988768C???????????
18402.41611469×10¹⁶2416114690688960C???????????
18503.15730322×10¹⁶3157303226823816C???????????
18604.12585834×10¹⁶4125858340963664C???????????
18705.39153488×10¹⁶5391534888544408C???????????
18807.04547969×10¹⁶7045479698166474C???????????
18909.20679943×10¹⁶9206799438350900C???????????
19001.20311414×10¹⁷12031141468524498C???????????
19101.57218920×10¹⁷15721892011040152C???????????
19202.05448624×10¹⁷20544862456681992C???????????
19302.68473451×10¹⁷26847345140511656C???????????
19403.50832201×10¹⁷35083220134388846C???????????
19504.58456072×10¹⁷45845607244178780C???????????
19605.99095441×10¹⁷59909544174380652C???????????
19707.82877757×10¹⁷78287775777012988C???????????
19801.02303901×10¹⁸102303901323164112C???????????
19901.33687366×10¹⁸133687366357032876C???????????
20001.74698222×10¹⁸174698222664339800C???????????
N>0xall?????

See Also

W pentomino and Y1 hexominoX pentomino and Y pentomino