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.


I triomino and X pentomino

Prime rectangles: ≥ 38.

Smallest rectangle tilings

Smallest rectangle (10x15):

Smallest square (15x15):

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 \ h1-9101112131415161718N>0
1-90
1000
11000
120000000
1300022P0
1400044P00
1502020P4444P7878P6502265022P208626208626P10556921055692P
16000734734P00102743210102743210P0
1700027242724P00472585290472585290P00
18044084408P1221612216P3170231702P6954338869543388P279098942279098942P2.57847869×10¹⁰2578478698P5.13627770×10¹²513627770174P2.97480419×10¹³2974804196382P2.71345553×10¹⁴27134555342140
19000226954226954P001.21660043×10¹²121660043264P002.74372199×10¹⁶27437219951317883k
2000010744441074444P007.41149698×10¹²741149698714C002.13750910×10¹⁷21375091028287630C3k
210595512595512P21820922182092P93863709386370P4.41220459×10¹¹44122045926P2.30772551×10¹²230772551722P4.42919412×10¹³4429194123374C1.48511557×10¹⁶1485115578755540P1.12527326×10¹⁷11252732631329542P1.97429946×10¹⁸197429946398296874Call
220006426659264266592P001.26740311×10¹⁵126740311965400C001.24577070×10²⁰12457707022319814482C3k
23000342671958342671958P009.51765962×10¹⁵951765962020048C00≥1.84467440×10²⁰≥18446744073709551615C3k
2406584118065841180P329850404329850404P2.54686663×10¹⁰2546866632P2.21673460×10¹⁴22167346057038C1.56524935×10¹⁵156524935500892C6.35099437×10¹⁶6350994378399740C3.32469142×10¹⁹3324691426389318880C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615Call
250001.71261624×10¹¹17126162446P001.25795197×10¹⁸125795197645077212C00≥1.84467440×10²⁰≥18446744073709551615C3k
260009.77850917×10¹¹97785091738C001.09072081×10¹⁹1090720815552388172C00≥1.84467440×10²⁰≥18446744073709551615C3k
2706.59153091×10¹⁰6591530912P4.60122526×10¹¹46012252668P6.65590737×10¹²665590737940C9.83249064×10¹⁶9832490645008504C9.61769092×10¹⁷96176909290519134C8.07171687×10¹⁹8071716874226135578C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615Call
280004.39360338×10¹³4393603385736C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C3k
290002.61075501×10¹⁴26107550135302C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C3k
3006.23891048×10¹²623891048934C6.12683086×10¹³6126830865958C1.69632839×10¹⁵169632839698222C4.05142576×10¹⁹4051425767555024338C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615Call
310001.09976517×10¹⁶1099765178619820C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C3k
320006.68060598×10¹⁶6680605986079338C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C3k
3305.69920168×10¹⁴56992016836016C7.91150192×10¹⁵791150192386000C4.23669192×10¹⁷42366919297448682C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615Call
340002.70531198×10¹⁸270531198372598902C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C3k
350001.66164482×10¹⁹1661644820594478144C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C3k
3605.07978943×10¹⁶5079789432327958C9.99333753×10¹⁷99933375308265182C1.04041084×10²⁰10404108405148814034C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615Call
37000≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C3k
38000≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C3k
3904.44623642×10¹⁸444623642905591364C1.24144363×10²⁰12414436308773208516C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615Call
40000≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C3k
41000≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C3k
420≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615Call
N>0x3k3kall3k3kall3k3kall

See Also

I triomino and W pentominoI triomino and Y pentomino