POLYOMINO TILINGS

Polyomino Tilings

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P3 9-omino

Area: 9.

Size: 2x7.

Is rectangular: no.

Is convex: yes.

Holes: 0.

Order: 2.

Odd order: ≤ 95.

Prime rectangles: ≥ 9.

Smallest rectangle tilings

Smallest rectangle (2x9):

Smallest known odd rectangles (15x57, 19x45):

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 \ h123456789101112131415161718192021N>0
10
200
3000
40000
500000
6000000
70000000
800000000
9022P044088016160
100000000032320
11000000000000
1200000000646400000
13000000000000000
14000000001281280000000
15000000000000000000
160000000025625600000000??
1700000000000000000????
180440161606464025625651251210241024409640964096409624576245761638416384131072131072??????
1900000000000000000????????
20000000001024102400000000??????????
21000000000000000000????????????
22000000002048204800000000?????????????
2300000000000000000?????????????
240000000040964096000000000?????????????
2500000000000000000?????????????
26000000008192819200000000?????????????
270880646405125120409640960327683276800262144262144002097152209715200?????????????
2800000000163841638400000000?????????????
2900000000000000000?????????????
30000000003276832768000000000?????????????
3100000000000000000?????????????
3200000000655366553600000000?????????????
33000000000000000000?????????????
340000000013107213107200000000?????????????
3500000000000000000?????????????
360161602562560409640960655366553626214426214410485761048576169082881690828816777216167772166081740806081740802684354562684354561.72805324×10¹¹17280532480?????????????
3700000000000000000?????????????
380000000052428852428800000000?????????????
39000000000000000000?????????????
40000000001048576104857600000000?????????????
4100000000000000000?????????????
420000000020971522097152000000000?????????????
4300000000000000000?????????????
44000000004194304419430400000000?????????????
45032320102410240327683276801048576104857603355443233554432001.07374182×10¹⁰1073741824003.43597383×10¹¹3435973836800??????≥1≥1P?????
46000000008388608838860800000000?????????????
4700000000000000000?????????????
48000000001677721616777216000000000?????????????
4900000000000000000?????????????
5000000000335544323355443200000000?????????????
51000000000000000000?????????????
5200000000671088646710886400000000?????????????
5300000000000000000?????????????
54064640409640960262144262144016777216167772161342177281342177281.07374182×10¹⁰10737418246.97963642×10¹¹697963642886.87194767×10¹¹687194767361.56519849×10¹⁴156519849000964.39804651×10¹³43980465111042.35638441×10¹⁶2356384414826496?????????????
5500000000000000000?????????????
560000000026843545626843545600000000?????????????
5700000000000000001.31941395×10¹⁴13194139533312P?????????????
580000000053687091253687091200000000?????????????
5900000000000000000?????????????
60000000001.07374182×10¹⁰1073741824000000000??????????≥1≥1P?
6100000000000000000?????????????
62000000002.14748364×10¹⁰214748364800000000?????????????
63012812801638416384020971522097152026843545626843545603.43597383×10¹¹34359738368004.39804651×10¹³4398046511104005.62949953×10¹⁵56294995342131200?????????????
64000000004.29496729×10¹⁰429496729600000000?????????????
6500000000000000000?????????????
66000000008.58993459×10¹⁰858993459200000009.53688898×10¹⁵953688898142208P?????????????
6700000000000000000?????????????
68000000001.71798691×10¹¹1717986918400000000?????????????
6900000000000000001.75921860×10¹⁴17592186044416P?????????????
70000000003.43597383×10¹¹3435973836800000000?????????????
7100000000000000000?????????????
720256256065536655360167772161677721604.29496729×10¹⁰42949672966.87194767×10¹¹687194767361.09951162×10¹³10995116277762.88115071×10¹⁵2881150716477442.81474976×10¹⁵2814749767106564.16728177×10¹⁸4167281775707422727.20575940×10¹⁷72057594037927936≥1.84467440×10²⁰≥18446744073709551615?????????????
7300000000000000000?????????????
74000000001.37438953×10¹²13743895347200000000?????????????
7500000000000000005.89619707×10¹⁹5896197074646466560?????????????
76000000002.74877906×10¹²27487790694400000000?????????????
7700000000000000000?????????????
78000000005.49755813×10¹²54975581388800000002.06928088×10¹⁷20692808834744320P?????????????
7900000000000000000?????????????
80000000001.09951162×10¹³109951162777600000000?????????????
8105125120262144262144013421772813421772806.87194767×10¹¹6871947673603.51843720×10¹⁴35184372088832001.80143985×10¹⁷18014398509481984009.22337203×10¹⁹922337203685477580800?????????????
82000000002.19902325×10¹³219902325555200000000?????????????
8300000000000000000?????????????
84000000004.39804651×10¹³43980465111040000000≥1.84467440×10²⁰≥18446744073709551615?????????????
8500000000000000000?????????????
86000000008.79609302×10¹³879609302220800000000?????????????
870000000000000000≥1.84467440×10²⁰≥18446744073709551615?????????????
88000000001.75921860×10¹⁴1759218604441600000000?????????????
8900000000000000000?????????????
9001024102401048576104857601.07374182×10¹⁰107374182401.09951162×10¹³10995116277763.51843720×10¹⁴351843720888321.12589990×10¹⁶11258999068426241.18932118×10¹⁹11893211824536944641.15292150×10¹⁹1152921504606846976≥1.84467440×10²⁰≥18446744073709551615≥1.84467440×10²⁰≥18446744073709551615≥1.84467440×10²⁰≥18446744073709551615?????????????
9100000000000000000?????????????
92000000007.03687441×10¹⁴7036874417766400000000?????????????
930000000000000000≥1.84467440×10²⁰≥18446744073709551615?????????????
94000000001.40737488×10¹⁵14073748835532800000000?????????????
9500000000000000000?????????????
96000000002.81474976×10¹⁵2814749767106560000000≥1.84467440×10²⁰≥18446744073709551615?????????????
9700000000000000000?????????????
98000000005.62949953×10¹⁵56294995342131200000000?????????????
9902048204804194304419430408.58993459×10¹⁰858993459201.75921860×10¹⁴1759218604441603.60287970×10¹⁷3602879701896396800≥1.84467440×10²⁰≥1844674407370955161500≥1.84467440×10²⁰≥184467440737095516159.96196237×10¹⁹9961962375743537152P?????????????
100000000001.12589990×10¹⁶112589990684262400000000?????????????
10100000000000000000?????????????
102000000002.25179981×10¹⁶22517998136852480000000≥1.84467440×10²⁰≥18446744073709551615?????????????
10300000000000000000?????????????
104000000004.50359962×10¹⁶450359962737049600000000?????????????
1050000000000000000≥1.84467440×10²⁰≥18446744073709551615?????????????
106000000009.00719925×10¹⁶900719925474099200000000?????????????
10700000000000000000?????????????
1080409640960167772161677721606.87194767×10¹¹6871947673602.81474976×10¹⁵2814749767106561.80143985×10¹⁷180143985094819841.15292150×10¹⁹1152921504606846976≥1.84467440×10²⁰≥18446744073709551615≥1.84467440×10²⁰≥18446744073709551615≥1.84467440×10²⁰≥18446744073709551615≥1.84467440×10²⁰≥18446744073709551615≥1.84467440×10²⁰≥18446744073709551615?????????????
10900000000000000000?????????????
110000000003.60287970×10¹⁷3602879701896396800000000?????????????
1110000000000000000≥1.84467440×10²⁰≥18446744073709551615?????????????
112000000007.20575940×10¹⁷7205759403792793600000000?????????????
11300000000000000000?????????????
114000000001.44115188×10¹⁸1441151880758558720000000≥1.84467440×10²⁰≥18446744073709551615?????????????
11500000000000000000?????????????
116000000002.88230376×10¹⁸28823037615171174400000000?????????????
1170819281920671088646710886405.49755813×10¹²54975581388804.50359962×10¹⁶45035996273704960≥1.84467440×10²⁰≥1844674407370955161500≥1.84467440×10²⁰≥1844674407370955161500≥1.84467440×10²⁰≥18446744073709551615≥1.84467440×10²⁰≥18446744073709551615?????????????
118000000005.76460752×10¹⁸57646075230342348800000000?????????????
11900000000000000000?????????????
120000000001.15292150×10¹⁹11529215046068469760000000≥1.84467440×10²⁰≥18446744073709551615?????????????
12100000000000000000?????????????
122000000002.30584300×10¹⁹230584300921369395200000000?????????????
1230000000000000000≥1.84467440×10²⁰≥18446744073709551615?????????????
124000000004.61168601×10¹⁹461168601842738790400000000?????????????
12500000000000000000?????????????
12601638416384026843545626843545604.39804651×10¹³439804651110407.20575940×10¹⁷720575940379279369.22337203×10¹⁹9223372036854775808≥1.84467440×10²⁰≥18446744073709551615≥1.84467440×10²⁰≥18446744073709551615≥1.84467440×10²⁰≥18446744073709551615≥1.84467440×10²⁰≥18446744073709551615≥1.84467440×10²⁰≥18446744073709551615≥1.84467440×10²⁰≥18446744073709551615?????????????
12700000000000000000?????????????
12800000000≥1.84467440×10²⁰≥1844674407370955161500000000?????????????
1290000000000000000≥1.84467440×10²⁰≥18446744073709551615?????????????
13000000000≥1.84467440×10²⁰≥1844674407370955161500000000?????????????
13100000000000000000?????????????
13200000000≥1.84467440×10²⁰≥184467440737095516150000000≥1.84467440×10²⁰≥18446744073709551615?????????????
13300000000000000000?????????????
13400000000≥1.84467440×10²⁰≥1844674407370955161500000000?????????????
1350327683276801.07374182×10¹⁰107374182403.51843720×10¹⁴3518437208883201.15292150×10¹⁹11529215046068469760≥1.84467440×10²⁰≥1844674407370955161500≥1.84467440×10²⁰≥18446744073709551615≥1.84467440×10²⁰≥18446744073709551615P≥1.84467440×10²⁰≥18446744073709551615≥1.84467440×10²⁰≥18446744073709551615?????????????
N>0x9kx9kx9kx9k2k9k??9k9k3k??????

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
P3 9-omino10000000

See Also

P2 9-ominoMonominoes and Dominoes