Tiling by Squares
Squared Squares
Simple Perfects
Simple Perfect Squared Squares (SPSSs)
SPSSs Order 21
(1) SPSSs Order 21
SPSSs Order 22
(8) SPSSs Order 22
SPSSs Order 23
(12) SPSSs Order 23
SPSSs Order 24
(26) SPSSs Order 24
SPSSs Order 25
(160) SPSSs Order 25
SPSSs Order 26
(441) SPSSs Order 26
SPSSs Order 27
(1152) SPSSs Order 27
SPSSs Order 28
(3001) SPSSs Order 28
SPSSs Order 28; 201A->774B
SPSSs Order 28; 774C->1108C
SPSSs Order 28; 1111A->1544A
SPSSs Order 29
(7901) SPSSs Order 29
SPSSs Order 29; 221A->828B
SPSSs Order 29; 828C->1136P
SPSSs Order 29; 1136Q->1532C
SPSSs Order 29; 1532D->2134A
SPSSs Order 30
(20566) SPSSs Order 30
SPSSs Order 30; 201A->884K
SPSSs Order 30; 884L->1196A
SPSSs Order 30; 1196B->1506P
SPSSs Order 30; 1506Q->2007S
SPSSs Order 30; 2008A->2710B
SPSSs Order 31
(54541) SPSSs Order 31
SPSSs Order 31; 215A->783D
SPSSs Order 31; 783E->1005L
SPSSs Order 31; 1006A->1224S
SPSSs Order 31; 1224T->1412N
SPSSs Order 31; 1412O->1657A
SPSSs Order 31; 1657B->1868D
SPSSs Order 31; 1868E->2004F
SPSSs Order 31; 2004G->2263A
SPSSs Order 31; 2263B->2768A
SPSSs Order 31; 2768B->3443A
SPSSs Order 32
(144161) SPSSs Order 32
SPSSs Order 32; 185A->747C
SPSSs Order 32; 747D->918L
SPSSs Order 32; 918M->1075V
SPSSs Order 32; 1075W->1212AF
SPSSs Order 32; 1212AG->1335U
SPSSs Order 32; 1335V->1473K
SPSSs Order 32; 1473L->1610G
SPSSs Order 32; 1610H->1743B
SPSSs Order 32; 1743C->1860Y
SPSSs Order 32; 1860Z->1999E
SPSSs Order 32; 1999F->2189K
SPSSs Order 32; 2189L->2348C
SPSSs Order 32; 2348D->2455Z
SPSSs Order 32; 2455AA->2543Q
SPSSs Order 32; 2543R->2636H
SPSSs Order 32; 2636I->2761A
SPSSs Order 32; 2761B->3249F
SPSSs Order 32; 3249G->3545F
SPSSs Order 32; 3545G->3758N
SPSSs Order 32; 3758O->4611A
SPSSs Order 33
(378197) SPSSs Order 33
SPSSs Order 34
(990981) SPSSs Order 34
SPSSs Order 35
(2578081) SPSSs Order 35
SPSSs Orders 36 - 39
(6674067) SPSSs Order 36
(17086918) SPSSs Order 37
(206856) SPSSs Order 38
(416502) SPSSs Order 39
SPSSs Orders 40 - 49
(806996) SPSSs Order 40
(1513270) SPSSs Order 41
(2674474) SPSSs Order 42
(4260645) SPSSs Order 43
(5124154) SPSSs Order 44
(2039) SPSSs Order 45
(2500) SPSSs Order 46
(2886) SPSSs Order 47
(3437) SPSSs Order 48
(4014) SPSSs Order 49
SPSSs Orders 50 - 59
(4550) SPSSs Order 50
(4872) SPSSs Order 51
(5608) SPSSs Order 52
(6155) SPSSs Order 53
(6908) SPSSs Order 54
(6983) SPSSs Order 55
(8395) SPSSs Order 56
(10186) SPSSs Order 57
(13819) SPSSs Order 58
(20340) SPSSs Order 59
SPSSs Orders 60 - 69
(29288) SPSSs Order 60
(49227) SPSSs Order 61
(86624) SPSSs Order 62
(150143) SPSSs Order 63
(244714) SPSSs Order 64
(382299) SPSSs Order 65
(379731) SPSSs Order 66
(188128) SPSSs Order 67
(28737) SPSSs Order 68
(39440) SPSSs Order 69
SPSSs Orders 70 - 79
(56990) SPSSs Order 70
(78937) SPSSs Order 71
(105047) SPSSs Order 72
(127896) SPSSs Order 73
(135197) SPSSs Order 74
(114999) SPSSs Order 75
(54923) SPSSs Order 76
(6042) SPSSs Order 77
(7521) SPSSs Order 78
(9008) SPSSs Order 79
SPSSs Orders 80 - 89
(11188) SPSSs Order 80
(12561) SPSSs Order 81
(12876) SPSSs Order 82
(11628) SPSSs Order 83
(8338) SPSSs Order 84
(4069) SPSSs Order 85
(63) SPSSs Order 86
(47) SPSSs Order 87
(40) SPSSs Order 88
(35) SPSSs Order 89
SPSSs Orders 90 - 99
(18) SPSSs Order 90
(13) SPSSs Order 91
(1) SPSSs Order 92
(8) SPSSs Order 93
(8) SPSSs Order 94
(4) SPSSs Order 95
(3) SPSSs Order 96
(2) SPSSs Order 97
(1) SPSSs Order 98
(2) SPSSs Order 99
SPSSs Orders 100 - 109
(5) SPSSs Order 100
(3) SPSSs Order 101
(3) SPSSs Order 102
(1) SPSSs Order 103
(2) SPSSs Order 104
(2) SPSSs Order 105
(1) SPSSs Order 106
(1) SPSSs Order 107
(1) SPSSs Order 108
(1) SPSSs Order 109
SPSSs Orders 110 - 119
(1) SPSSs Order 110
(1) SPSSs Order 111
(2) SPSSs Order 112
(1) SPSSs Order 113
(1) SPSSs Order 114
(1) SPSSs Order 115
(2) SPSSs Order 116
(1) SPSSs Order 117
(1) SPSSs Order 118
(2) SPSSs Order 119
SPSSs Orders 120 - 129
(1) SPSSs Order 120
(2) SPSSs Order 121
(1) SPSSs Order 122
(2) SPSSs Order 123
(1) SPSSs Order 124
(2) SPSSs Order 125
(1) SPSSs Order 126
(1) SPSSs Order 127
(2) SPSSs Order 128
(2) SPSSs Order 129
SPSSs Orders 130 - 236
(1) SPSSs Order 130
(1) SPSSs Order 133
(1) SPSSs Order 140
(1) SPSSs Order 169
(1) SPSSs Order 208
(1) SPSSs Order 216
(1) SPSSs Order 220
(1) SPSSs Order 236
Simple Imperfects
Simple Imperfect Squared Squares (SISSs)
SISS Order 13
(1) SISS Order 13
SISS Order 15
(3) SISSs Order 15
SISS Order 16
(5) SISSs Order 16
SISS Order 17
(15) SISSs Order 17
SISS Order 18
(19) SISSs Order 18
SISS Order 19
(57) SISSs Order 19
SISS Order 20
(72) SISSs Order 20
SISS Order 21
(274) SISSs Order 21
SISS Order 22
(491) SISSs Order 22
Compound Perfects
Compound Perfect Squared Squares (CPSSs)
CPSS Order 24
(1/4) CPSS Order 24
CPSS Order 25
(2/12) CPSSs Order 25
CPSS Order 26
(16/100) CPSSs Order 26
CPSS Order 27
(46/220) CPSSs Order 27
CPSS Order 28
(143/948) CPSSs Order 28
CPSS Order 29
(412/2308) CPSSs Order 29
CPSS Order 30
(941/5668) CPSSs Order 30
CPSS Order 31
(2788/17351) CPSSs Order 31
CPSS Order 32
(7941/52196) CPSSs Order 32
CPSS Order 33
(22413/150669) CPSSs Order 33
CPSS Order 34
(62273/429458) CPSSs Order 34
CPSS Order 35
(172330/1206181) CPSSs Order 35
CPSS Order 36
(466508/3337989) CPSSs Order 36
CPSS Order 37- 39
(1239742/8961794) CPSSs Order 37
(3257378/23989218) CPSSs Order 38
(8430928/62894424) CPSSs Order 39
CPSS Order 40 - 49
(5563) CPSSs Order 40
(635) CPSSs Order 41
(4410) CPSSs Order 42
(1797) CPSSs Order 43
(7099) CPSSs Order 44
(417) CPSSs Order 45
(1136) CPSSs Order 46
(2605) CPSSs Order 47
(5013) CPSSs Order 48
(9403) CPSSs Order 49
CPSS Order 50 - 59
(4035) CPSSs Order 50
(5668) CPSSs Order 51
(8901) CPSSs Order 52
(5733) CPSSs Order 53
(7092) CPSSs Order 54
(7495) CPSS Order 55
(7608) CPSSs Order 56
(6331) CPSSs Order 57
(4592) CPSS Order 58
(2504) CPSS Order 59
CPSS Order 60 - 69
(69) CPSS Order 60
(4) CPSS Order 61
(1) CPSS Order 62
(4) CPSS Order 63
(6) CPSS Order 64
(1) CPSS Order 65
(4) CPSS Order 66
(2) CPSS Order 68
(2) CPSS Order 69
CPSS Order 70 - 79
(2) CPSS Order 70
(1) CPSS Order 71
(1) CPSS Order 76
(3) CPSS Order 79
CPSS Order 81 - 86
(2) CPSS Order 81
(1) CPSS Order 85
(2) CPSS Order 86
Mrs Perkins's Quilts
Mrs Perkins's Quilts
'Special' Squared Squares
'Special' Perfect Squared Squares
Squared Square Downloads
Squared Square Downloads
Squared Rectangles
Simple Perfects
Simple Perfect Squared Rectangles (SPSRs)
SPSRs Order 9
(2) SPSRs Order 9
SPSRs Order 10
(6) SPSRs Order 10
SPSRs Order 11
(22) SPSRs Order 11
SPSRs Order 12
(67) SPSRs Order 12
SPSRs Order 13
(213) SPSRs Order 13
SPSRs Order 14
(744) SPSRs Order 14
SPSRs Order 15
(2609) SPSRs Order 15
SPSRs Order 16
(9016) SPSRs Order 16
(1000) 75x73A->743x686A
(1000) 743x686B->1253x1216A
(1000) 1253x1240A->1464x1223A
(1000) 1464x1223B->2434x2235A
(1000) 2434x2265A->2615x2456A
(1000) 2615x2459A->2743x2723A
(1000) 2743x2731A->2881x2109A
(1000) 2881x2145A->3037x2184A
(1016) 3037x2190A ->3581x2675A
SPSRs Order 17
(31426) SPSRs Order 17
(1000) 82 x 75A -> 510 x 487A
(1000) 510 x 500A -> 709 x 532A
(1000) 709 x 533A -> 891 x 637A
(1000) 891 x 686A -> 1114 x 1020A
(1000) 1114 x 1110A -> 1338 x 1274A
(1000) 1338 x 1310A -> 1542 x 1273A
(1000) 1542 x 1273B -> 1753 x 1047A
(1000) 1753 x 1062A -> 2123 x 2119A
(1000) 2123 x 2122A -> 2258 x 2242B
(1000) 2258 x 2242C -> 2369 x 1793A
(1000) 2369 x 1808A -> 2471 x 1808A
(1000) 2471 x 1831A -> 2612 x 2343A
(1000) 2612 x 2438A -> 2840 x 1678A
(1000) 2840 x 1918A -> 3949 x 3792A
(1000) 3949 x 3830A -> 4123 x 3583A
(1000) 4123 x 3678A -> 4234 x 4003A
(1000) 4234 x 4011A -> 4335 x 3919A
(1000) 4335 x 3953A -> 4414 x 3951A
(1000) 4414 x 4031A -> 4492 x 4435A
(1000) 4493 x 3723A -> 4562 x 4139A
(1000) 4562 x 4139B -> 4628 x 4613B
(1000) 4629 x 3760A -> 4699 x 3978A
(1000) 4699 x 4060A -> 4771 x 3112A
(1000) 4771 x 3179A -> 4834 x 4535A
(1000) 4834 x 4571A -> 4915 x 4253A
(1000) 4915 x 4373A -> 4996 x 4469A
(1000) 4997 x 4359A -> 5071 x 2264A
(1000) 5071 x 3056A -> 5151 x 4894A
(1000) 5151 x 5149A -> 5289 x 4009A
(1000) 5289 x 4102A -> 5421 x 3632A
(1000) 5421 x 3634A -> 5686 x 4399A
(426) 5686 x 4469A -> 6256 x 4261A
SPSRs by Various Properties
Simple Perfects by semi-perimeter
Simple Perfects by difference
Simple Perfects by aspect
Simple Perfects by isomer
SPSRs by disjoint n-tuple
SPSRs by element min/max
SPSRs by prime elements
SPSRs with crosses
SPSRs with boundary rules
Simple Imperfects
Simple Imperfect Squared Rectangles (SISRs)
SISRs Order 9
(1) SISRs Order 9
SISRs Order 12
(9) SISRs Order 12
SISRs Order 13
(33) SISRs Order 13
SISRs Order 14
(104) SISRs Order 14
SISRs Order 15
(280) SISRs Order 15
SISRs Order 16
(948) SISRs Order 16
SISRs Order 17
(3014) SISRs Order 17
SISRs Order 18
(9494) SISRs Order 18
SISRs Order 19
(30302) SISRs Order 19
SISRs Order 20
(98897) SISRs Order 20
Squared Rectangle Downloads
Squared Rectangle Downloads
Squared Open Surfaces
Squared Cylinders (SPSCs)
Squared Möbius Strips
Squared Cones
Squared Periodic Tilings
Squared Tori
Squared Klein Bottles
Squared Projective Planes
Squaring the Plane
Squaring the Plane I
Squaring the Plane II
History and Theory
Squaring the Square, Introduction
Ernest Dudeney
Max Dehn
Zbigniew Moroń
Sam Loyd
Michio Abe
RP Sprague
Brooks, Smith, Stone, Tutte I
Brooks, Smith, Stone, Tutte II
CJ Bouwkamp
AJW Duijvestijn
Martin Gardner
TH Willcocks,
PJ Federico
JC Wilson
P Leeuw
GH Morley
JD Skinner II
I Gambini
S Anderson
B Trial
Ed Pegg
S Johnson
L Milla
JB Williams
BL Moss
K Scott
Tiling by Triangles
Tiling by Triangles
Triangled Equilateral Triangles
Equilateral Triangle Dissections
Isosceles Right Triangled Squares
Isosceles Right Triangled Squares
Primitive Perfects
Derivative Ultraperfects
Non-ultraperfect Perfects
Simple Primitive Imperfects
Software
Software and utilities for squared tilings
Related Links and Artwork
Links
The Bill Tutte Memorial Fund