POLYOMINO TILINGS

Polyomino Tilings

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P1 11-omino

Area: 11.

Size: 3x5.

Is rectangular: no.

Is convex: yes.

Holes: 0.

Order: ≤ 270.

Odd order: ≤ 423.

Prime rectangles: ≥ 2.

Smallest rectangle tilings

Smallest known rectangle (54x55):

Smallest known odd rectangle (47x99):

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 \ h1-2930313233343536373839404142434445464748495051525354N>0
1-290
3000
3100??
3200????
33000??????
3400????????
3500??????????
3600????????????
3700??????????????
3800????????????????
3900??????????????????
4000????????????????????
4100??????????????????????
4200????????????????????????
4300??????????????????????????
44000????????????????????????????
4500??????????????????????????????
4600????????????????????????????????
4700??????????????????????????????????
4800????????????????????????????????????
4900??????????????????????????????????????
5000????????????????????????????????????????
5100??????????????????????????????????????????
5200????????????????????????????????????????????
5300??????????????????????????????????????????????
5400????????????????????????????????????????????????
55000??????????????????????????????????????????????≥1≥1P?
5600?????????????????????????????????????????????????
5700?????????????????????????????????????????????????
5800?????????????????????????????????????????????????
5900?????????????????????????????????????????????????
6000?????????????????????????????????????????????????
6100?????????????????????????????????????????????????
6200?????????????????????????????????????????????????
6300?????????????????????????????????????????????????
6400?????????????????????????????????????????????????
6500?????????????????????????????????????????????????
66000?????????????????????????????????????????????????
6700?????????????????????????????????????????????????
6800?????????????????????????????????????????????????
6900?????????????????????????????????????????????????
7000?????????????????????????????????????????????????
7100?????????????????????????????????????????????????
7200?????????????????????????????????????????????????
7300?????????????????????????????????????????????????
7400?????????????????????????????????????????????????
7500?????????????????????????????????????????????????
7600?????????????????????????????????????????????????
77000?????????????????????????????????????????????????
7800?????????????????????????????????????????????????
7900?????????????????????????????????????????????????
8000?????????????????????????????????????????????????
8100?????????????????????????????????????????????????
8200?????????????????????????????????????????????????
8300?????????????????????????????????????????????????
8400?????????????????????????????????????????????????
8500?????????????????????????????????????????????????
8600?????????????????????????????????????????????????
8700?????????????????????????????????????????????????
88000?????????????????????????????????????????????????
8900?????????????????????????????????????????????????
9000?????????????????????????????????????????????????
9100?????????????????????????????????????????????????
9200?????????????????????????????????????????????????
9300?????????????????????????????????????????????????
9400?????????????????????????????????????????????????
9500?????????????????????????????????????????????????
9600?????????????????????????????????????????????????
9700?????????????????????????????????????????????????
9800?????????????????????????????????????????????????
990??????????????????????????????????≥1≥1P???????????????
N>0x11k????????????????????????

Attributions

  1. Rectangles 47x99 and 54x55 taken from http://www.cflmath.com/~reid/Polyomino/11omino7_rect.html

See Also

MonominoesL1 12-omino