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.


P3 heptomino

Area: 7.

Size: 3x3.

Holes: 0.

Order: 28.

Square order: 28.

Odd order: 45.

Prime rectangles: ≥ 37.

Smallest rectangle tilings

Smallest rectangle and smallest square (14x14):

Smallest odd rectangle (15x21):

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 \ h1-101112131415161718192021N>0
1-100
1100
12000
130000
140000009696P
150000000
1600000000
17000000000
180000000000
190000640640P00000
20000031043104P000000
21000128128P000≥1000≥1000P≥1000≥1000P≥1000≥1000P≥1000≥1000P≥1≥1P≥1≥1P≥1≥1P
220000128128P000000???
23000015361536P000000???
24000076807680P000000≥1≥1C?
2500003817638176P000000???
260000123168123168P000000???
27000016641664P000000≥1≥1C?
2800081928192P03968039680C≥1000≥1000P≥1000≥1000P≥1000≥1000P≥1000≥1000P≥1≥1C≥1≥1C≥1≥1C?
290000172160172160P000000≥1≥1C?
300000606304606304P000000≥1≥1C?
31000021695362169536P000000≥1≥1C?
32000050108485010848P000000≥1≥1C?
330000727168727168C000000≥1≥1C?
34000041582084158208C000000≥1≥1C?
35020482048P276736276736P01408144014081440P≥1≥1P≥1≥1P≥1≥1P≥1≥1P≥1≥1C≥1≥1C≥1≥1C?
3600004233788842337888C000000≥1≥1C?
370000116141280116141280C000000≥1≥1C?
380000215708448215708448C000000≥1≥1C?
3900008507161685071616C000000≥1≥1C?
400000340132448340132448C000000≥1≥1C?
4100001.00919795×10¹⁰1009197952C000000≥1≥1C?
42011521152P43668484366848C02.63372787×10¹⁰2633727872C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
4300006.11236249×10¹⁰6112362496C000000≥1≥1C?
4400001.00037615×10¹¹10003761568C000000≥1≥1C?
4500007.63045814×10¹⁰7630458144C000000≥1≥1C?
4600002.50986282×10¹¹25098628256C000000≥1≥1C?
4700006.66477827×10¹¹66647782720C000000≥1≥1C?
4800001.56105462×10¹²156105462080C000000≥1≥1C?
4906144061440P177596928177596928C03.23486470×10¹²323486470944C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
5000005.07339950×10¹²507339950592C000000≥1≥1C?
5100005.97595227×10¹²597595227072C000000≥1≥1C?
5200001.72219158×10¹³1722191589600C000000≥1≥1C?
5300004.18563564×10¹³4185635645824C000000≥1≥1C?
5400009.04421722×10¹³9044217222688C000000≥1≥1C?
5500001.74963655×10¹⁴17496365592672C000000≥1≥1C?
5606451264512P4.07731724×10¹⁰4077317248C02.79531547×10¹⁴27953154783872C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
5700004.31138013×10¹⁴43113801331872C000000≥1≥1C?
5800001.12611669×10¹⁵112611669020768C000000≥1≥1C?
5900002.55178305×10¹⁵255178305277408C000000≥1≥1C?
6000005.20972878×10¹⁵520972878392704C000000≥1≥1C?
6100009.74800176×10¹⁵974800176062816C000000≥1≥1C?
6200001.63659356×10¹⁶1636593566441056C000000≥1≥1C?
63011079681107968P1.33008183×10¹²133008183808C02.94359781×10¹⁶2943597810518656C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
6400007.12732295×10¹⁶7127322955313920C000000≥1≥1C?
6500001.53073145×10¹⁷15307314506063648C000000≥1≥1C?
6600003.01462696×10¹⁷30146269687164640C000000≥1≥1C?
6700005.59706196×10¹⁷55970619646990080C000000≥1≥1C?
6800009.93239360×10¹⁷99323936037043104C000000≥1≥1C?
6900001.93422722×10¹⁸193422722527831872C000000≥1≥1C?
70091852809185280C4.16378133×10¹³4163781330944C04.41538784×10¹⁸441538784107485088C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
N>0x7k7kxall7k7k7k7k7k7kall

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
P3 heptomino1000000

See Also

P2 heptominoP4 heptomino