POLYOMINO TILINGS

Polyomino Tilings

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You may also see list of all polyomino sets for which data is available here.


I triomino

Area: 3.

Perimeter: 8.

Size: 1x3.

Is rectangular: yes.

Is convex: yes.

Holes: 0.

Order: 1.

Square order: 3.

Odd order: 1.

Prime rectangles: 1.

Smallest rectangle tilings

Smallest rectangle and smallest odd rectangle (1x3):

Smallest square (3x3):

Rectangle tilings' solutions count (including symmetric)

Blue number - strongly prime rectangle (which cannot be divided into two or more number of rectangles tileable by this set).

Green number - weakly prime rectangle (which cannot be divided into two rectangles tileable by this set, but which can be divided into three or more rectangles).

Purple number - prime rectangle (unknown if weakly or strongly prime).

Red number - 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 \ h
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
N>0
1
0
2
0
0
3
1
1
2
4
0
0
3
0
5
0
0
4
0
0
6
1
1
6
13
22
64
7
0
0
9
0
0
155
0
8
0
0
13
0
0
321
0
0
9
1
1
19
57
121
783
2861
8133
37160
10
0
0
28
0
0
1888
0
0
143419
0
11
0
0
41
0
0
4233
0
0
468816
0
0
12
1
1
60
249
664
9912
52817
204975
1876855
≥1
≥1
≥1
13
0
0
88
0
0
23494
0
0
≥1
0
0
≥1
0
14
0
0
129
0
0
54177
0
0
≥1
0
0
≥1
0
0
15
1
1
189
1087
3643
126019
972557
5158223
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
0
0
277
0
0
295681
0
0
≥1
0
0
≥1
0
0
≥1
0
17
0
0
406
0
0
687690
0
0
≥1
0
0
≥1
0
0
≥1
0
0
18
1
1
595
4745
19987
1600185
17892281
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
0
872
0
0
3738332
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
20
0
0
1278
0
0
8712992
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
21
1
1
1873
20713
109657
20293761
≥151109437
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
22
0
0
2745
0
0
47337405
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
3k
23
0
0
4023
0
0
110368563
0
0
≥1
0
0
≥1
0
0
≥1
0
0
≥1
0
0
3k
24
1
1
5896
90417
601624
257206012
≥2.78963548×10¹⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
N>0
3k
3k
all
3k
3k
all
3k
3k
all
3k
3k
all
3k
3k
all
3k
3k
all
3k
3k

Smallest prime reptiles

Smallest prime reptile (3Ix2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
I triomino
1
1
19
249
3643
1600185

Smallest tori tilings

Smallest torus and smallest odd torus (1x3):

Smallest square torus (3x3):

Tori tilings' solutions count (including translations)

w \ h
1
2
3
4
5
6
7
8
9
1
0
2
0
0
3
3
9
54
4
0
0
93
0
5
0
0
288
0
0
6
3
9
918
201
678
4692
7
0
0
2775
0
0
9369
0
8
0
0
8613
0
0
34449
0
0
9
3
9
26757
921
3213
138411
98535
478017
≥500000

Smallest Baiocchi figures

Smallest Baiocchi figure (area 9):

See Also

TriominoesL triomino