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 pentomino and U pentomino

Prime rectangles: ≥ 5.

Smallest rectangle tilings

Smallest rectangle (4x5):

Smallest square (10x10):

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 \ h1-3456789101112131415N>0
1-30
400
5066P00
6002626P0
7000000
800116116C000
900000000
1009292C456456C13421342C54085408P2332223322C150994150994C714516714516C
110000000027498922749892C0
120017721772C00001239134012391340C00
13000000005481735254817352C000
140067366736C0000285933932285933932C0000
15010981098C006088860888C141408141408P45104764510476C3609752436097524P1.28391415×10¹⁰1283914156C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C
16002546425464C00005.74813755×10¹⁰5748137552C0000≥1000≥1000C5k
17000000002.58328832×10¹¹25832883298C0000≥1000≥1000C5k
18009578495784C00001.20292282×10¹²120292282608C0000≥1000≥1000C5k
19000000005.71919754×10¹²571919754150C0000≥1000≥1000C5k
2001224812248C359616359616C27695622769562C5004393250043932C913602756913602756C4.53134169×10¹¹45313416918C2.63532870×10¹³2635328707734C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
21000000001.20864790×10¹⁴12086479066174C0000≥1000≥1000C5k
220013484481348448C00005.56800503×10¹⁴55680050342638C0000≥1000≥1000C5k
23000000002.59502745×10¹⁵259502745740066C0000≥1000≥1000C5k
240050533285053328C00001.21505098×10¹⁶1215050984958798C0000≥1000≥1000C5k
250133528133528C00128733982128733982C2.51230579×10¹⁰2512305792C1.93857164×10¹²193857164094C2.08451550×10¹⁴20845155006612C5.63968256×10¹⁶5639682565847500C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
26001893091218930912C00002.61689288×10¹⁷26168928809307116C0000≥1≥1C5k
27000000001.21585766×10¹⁸121585766290601876C0000≥1≥1C5k
28007090736070907360C00005.67471246×10¹⁸567471246457934688C0000≥1≥1C5k
29000000002.64967360×10¹⁹2649673606571063234C0000≥1≥1C5k
30014437801443780C265564192265564192C6.11570467×10¹⁰6115704670C4.79379819×10¹²479379819024C4.27802260×10¹⁴42780226084366C1.66295305×10¹⁷16629530503843442C1.23505094×10²⁰12350509483342883558C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
N>0x5k?5k5k5k5kall5k5k5k5kall

See Also

L pentomino and T pentominoL pentomino and V pentomino