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.


N pentomino and I2 octomino

Prime rectangles: ≥ 32.

Smallest rectangle tilings

Smallest rectangle and smallest square (16x16):

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 \ h1-910111213141516N>0
1-90
10000
110000
12000000
1300000000
140000000000
15000000000000
160000000000001616
17000000000000???
18000000000000???
190000000000?????
2000000000???????
2100000000???????
2200000000???????
23000022?????????
24000000?????????
25000088?????????
26000022?????????
2700009898?????????
28000088?????????
290000478478?????????
300000108108?????????
31000036543654?????????
320000522522?????????
3300001937819378?????????
34000044404440?????????
35022P0123354123354?????????
36022P02291222912?????????
370000673016673016?????????
380000158000158000?????????
3904848P039434023943402?????????
4007878P0844256844256?????????
4100002160127821601278?????????
42000051806545180654?????????
430856856P0121436894121436894?????????
44018861886P02813259428132594?????????
450000661990880661990880?????????
460000162250520162250520?????????
4701385613856P03.63708794×10¹⁰3637087940?????????
4803652636526P0883016138883016138?????????
49022P01.96832445×10¹¹19683244598?????????
50022P04.92187094×10¹⁰4921870942?????????
510212288212288P01.06631067×10¹²106631067270?????????
520626838626838P02.68040183×10¹¹26804018306?????????
530124124P05.72946812×10¹²572946812382?????????
5409696P01.46183362×10¹²146183362066?????????
55031439243143924P03.07438497×10¹³3074384971500?????????
5601001057210010572P0≥1≥1?????????
57039023902P01.64150436×10¹⁴16415043698948?????????
58029802980P0≥1≥1?????????
5904546960045469600P08.74689066×10¹⁴87468906607652?????????
600152645328152645328P0≥1≥1?????????
6108992089920P04.64516285×10¹⁵464516285711372?????????
6206979469794P0≥1≥1?????????
630646045550646045550P02.46186309×10¹⁶2461863098256580?????????
6402.25493809×10¹⁰2254938096P0≥1≥1?????????
65017321641732164P01.30149278×10¹⁷13014927888970084?????????
66013616061361606P0≥1≥1?????????
6709.05335743×10¹⁰9053357432P06.86770946×10¹⁷68677094616434462?????????
6803.25550388×10¹¹32555038874P0≥1≥1?????????
6902989427829894278P03.61680954×10¹⁸361680954273219356?????????
7002369087623690876C0≥1≥1?????????
7101.25474401×10¹²125474401834C01.90163677×10¹⁹1901636773510389792?????????
720≥1≥1C0≥1≥1?????????
730480824630480824630P09.98216442×10¹⁹9982164424666105732?????????
740383072162383072162C0≥1≥1?????????
7501.72333684×10¹³1723336841564C0≥1≥1?????????
760≥1≥1C0≥1≥1?????????
7707.37723376×10¹⁰7377233762P0≥1≥1?????????
7805.89900890×10¹⁰5899008900C0≥1≥1?????????
7902.34913837×10¹⁴23491383747246C0≥1≥1?????????
800≥1≥1C0≥1≥1?????????
8101.09514803×10¹²109514803458P0≥1≥1?????????
8208.78050336×10¹¹87805033674C0≥1≥1?????????
8303.18180640×10¹⁵318180640681624C0≥1≥1?????????
840≥1≥1C0≥1≥1?????????
8501.58714666×10¹³1587146668672C0≥1≥1?????????
8601.27509870×10¹³1275098702390C0≥1≥1?????????
8704.28609024×10¹⁶4286090243886154C0≥1≥1?????????
880≥1≥1C0≥1≥1?????????
8902.25881596×10¹⁴22588159681212C0≥1≥1?????????
9001.81758125×10¹⁴18175812596996C0≥1≥1?????????
9105.74629504×10¹⁷57462950416888896C0≥1≥1?????????
920≥1≥1C0≥1≥1?????????
9303.16960904×10¹⁵316960904881150C0≥1≥1?????????
9402.55367754×10¹⁵255367754433668C0≥1≥1?????????
9507.67204101×10¹⁸767204101340327626C0≥1≥1?????????
960≥1≥1C0≥1≥1?????????
9704.39766130×10¹⁶4397661305460558C0≥1≥1?????????
9803.54672377×10¹⁶3546723771613554C0≥1≥1?????????
9901.02056872×10²⁰10205687294019852518C0≥1≥1?????????
1000≥1≥1C0≥1≥1?????????
N>0xallx?????

See Also

N pentomino and Y2 hexominoP pentomino and R pentomino