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.


P4 heptomino

Area: 7.

Size: 2x4.

Holes: 0.

Order: 2.

Square order: 28.

Odd order: 33.

Prime rectangles: 3.

Smallest rectangle tilings

Smallest rectangle (2x7):

Smallest square (14x14):

Smallest odd rectangle (11x21):

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 \ h1234567891011121314151617181920N>0
10
200
3000
40000
500000
6000000
7022P066C01616C0
80000004444C0
9000000000
10000000120120C000
1100000000000
12000000328328C00000
130000000000000
14044C04444C0320320C896896C27282728C92169216C2176021760C125584125584C178424178424C12506561250656C28921602892160C
1500000000000001286836812868368C0
1600000024482448C0000003285455232854552C00
170000000000000123029280123029280C000
1800000066886688C000000423800072423800072C0000
1900000000000001.16475825×10¹⁰1164758256C00000
200000001827218272C0000004.70098205×10¹⁰4700982056C000000
21088C0344344C066566656C0186272186272C0043018884301888C3232P109629642109629642C768768C1.34007916×10¹¹13400791688C10730481073048C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
220000004992049920C0000005.20777576×10¹¹52077757616C000000?
2300000000000001.45496252×10¹²145496252976C000000?
24000000136384136384C0000005.46412651×10¹²546412651080C000000?
2500000000000001.70241485×10¹³1702414857008C000000?
26000000372608372608C0000005.61955217×10¹³5619552174424C000000?
2700000000000001.90220919×10¹⁴19022091922784C000000?
2801616C027362736C0139264139264C10179841017984C1318368013183680C9812731698127316C866918912866918912C2.51276246×10¹¹25127624668C7.03792621×10¹¹70379262146C2.34234160×10¹³2342341608466C6.13044452×10¹⁴61304445235440C3.37442594×10¹⁵337442594094384C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
2900000000000002.13023322×10¹⁵213023322385352C000000?
3000000027811842781184C0000006.58726233×10¹⁵658726233515880C000000?
3100000000000002.31854075×10¹⁶2318540756806728C000000?
3200000075983367598336C0000007.34042059×10¹⁶7340420596710080C000000?
3300000000000002.48446967×10¹⁷24844696781612104C000000?
340000002075904020759040C0000008.09885738×10¹⁷80988573851435936C000000?
3503232C02185621856C029163522916352C0948071168948071168C001.75567440×10¹²175567440160C9519351295193512C4.62160664×10¹⁴46216066491130C6.65362901×10¹²665362901632C2.70476326×10¹⁸270476326150479704C1.03574384×10¹⁶1035743849426832C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
360000005671475256714752C0000008.98867963×10¹⁸898867963864372544C000000?
3700000000000002.92258540×10¹⁹2922585405174565296C000000?
38000000154947584154947584C0000009.86765911×10¹⁹9867659115786984896C000000?
390000000000000≥1.84467440×10²⁰≥18446744073709551615C000000?
40000000423324672423324672C000000≥1.84467440×10²⁰≥18446744073709551615C000000?
410000000000000≥1.84467440×10²⁰≥18446744073709551615C000000?
4206464C0174784174784C06107955261079552C1.15654451×10¹⁰1156544512C6.87261004×10¹¹68726100480C1.04484689×10¹³1044846893232C3.56141414×10¹⁴35614141412352C5.29587220×10¹⁶5295872205503258C3.07809779×10¹⁷30780977948547194C4.44002171×10¹⁹4440021711617339984C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
430000000000000≥1.84467440×10²⁰≥18446744073709551615C000000?
440000003.15973836×10¹⁰3159738368C000000≥1.84467440×10²⁰≥18446744073709551615C000000?
450000000000000≥1.84467440×10²⁰≥18446744073709551615C000000?
460000008.63256576×10¹⁰8632565760C000000≥1.84467440×10²⁰≥18446744073709551615C000000?
470000000000000≥1.84467440×10²⁰≥18446744073709551615C000000?
480000002.35846082×10¹¹23584608256C000000≥1.84467440×10²⁰≥18446744073709551615C000000?
490128128C013981441398144C01.27926272×10¹⁰1279262720C05.00527989×10¹³5005279899648C007.23021985×10¹⁶7230219856609440C3.84694185×10¹⁴38469418552432C≥1.84467440×10²⁰≥18446744073709551615C3.69385722×10¹⁹3693857224801258152C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
500000006.44343480×10¹¹64434348032C000000≥1.84467440×10²⁰≥18446744073709551615C000000?
510000000000000≥1.84467440×10²⁰≥18446744073709551615C000000?
520000001.76037912×10¹²176037912576C000000≥1.84467440×10²⁰≥18446744073709551615C000000?
530000000000000≥1.84467440×10²⁰≥18446744073709551615C000000?
540000004.80944521×10¹²480944521216C000000≥1.84467440×10²⁰≥18446744073709551615C000000?
550000000000000≥1.84467440×10²⁰≥18446744073709551615C000000?
560256256C01118489611184896C02.67932139×10¹¹26793213952C1.31396486×10¹³1313964867584C3.65704894×10¹⁵365704894709760C1.11253995×10¹⁷11125399539769360C1.46870266×10¹⁹1468702664246410272C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
570000000000000≥1.84467440×10²⁰≥18446744073709551615C000000?
580000003.58981877×10¹³3589818777600C000000≥1.84467440×10²⁰≥18446744073709551615C000000?
590000000000000≥1.84467440×10²⁰≥18446744073709551615C000000?
600000009.80756729×10¹³9807567290368C000000≥1.84467440×10²⁰≥18446744073709551615C000000?
610000000000000≥1.84467440×10²⁰≥18446744073709551615C000000?
620000002.67947721×10¹⁴26794772135936C000000≥1.84467440×10²⁰≥18446744073709551615C000000?
630512512C08947865689478656C05.61164320×10¹²561164320768C02.67883023×10¹⁷26788302359283712C1555215552P≥1.84467440×10²⁰≥18446744073709551615C1.20208994×10²⁰12020899409672830972C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
N>0x7kx7kx7k2k7k7k7k7k7k7kall7k7k7k7k7k7k

Smallest prime reptiles

Smallest prime reptile (7P4x4):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²10²11²
P4 heptomino10048P0784P?≥1P?≥1P≥1P

See Also

P3 heptominoU heptomino