List of common objects by symmetry

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This page lists the ranking of each object in each symmetry on Catagolue. Only symmetries by the literal definition of the word are included; Catagolue calls everything a symmetry even if it's something else entirely.

Object C1 C2_1 C2_2 C2_4 C4_1 C4_4 D2_x D4_x1 D4_x4 D2_+1 D2_+2 D4_+1 D4_+2 D4_+4 D8_1 D8_4
Block 1 1 1 1 1 1 1 1 1 1 2 1 2 2 2 1
Blinker[note 1] 2 2 2 2 2 2 2 2 2 2 1 2 1 1 1 2
Beehive 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
Glider[note 2] 4 4 4 4 4 4 5 8 7 6 6 6 6 6 10 10
Loaf 5 5 5 5 5 5 4 4 4 4 4 4 4 4 4 4
Boat 6 6 6 6 6 6 6 5 5 5 5 5 5 5 5 5
Ship 7 7 7 7 7 7 7 6 6 7 7 7 7 8 7 7
Tub 8 8 8 8 8 9 9 9 9 8 8 8 8 9 8 9
Pond 9 9 9 9 9 8 10 10 10 9 9 9 9 7 9 8
Long boat 10 10 10 10 10 10 13 13 13 10 10 10 10 10 15 16
Toad 11 11 11 11 11 11 14 16 16 11 11 11 11 11 18 17
Ship-tie 12 12 12 12 12 12 12 12 12 12 12 13 12 12 12 12
Beacon 13 13 13 13 14 13 8 7 8 15 14 17 15 14 6 6
Barge 14 14 14 14 13 14 17 17 17 14 13 14 14 13 16 15
Half-bakery 15 15 15 15 15 15 15 15 15 16 15 18 16 17 14 14
Mango 16 17 16 16 16 16 20 21 20 19 17 21 21 19 26 24
Eater 1 17 16 17 17 17 17 22 23 23 21 20 23 24 20 32 28
Lightweight spaceship[note 2] 18 19 19 18 19 18 26 32 36 24 21 27 30 23 53 48
Long barge 19 20 20 19 18 19 11 11 11 25 23 26 29 22 11 11
Aircraft carrier 20 21 18 20 20 20 25 26 26 26 22 25 28 21 39 32
Pulsar 21 18 21 21 21 21 27 31 35 13 19 12 13 18 17 29
Paperclip 22 22 22 23 22 22 30 36 39 28 24 33 31 24 55 49
Middleweight spaceship[note 2] 23 24 24 26 25 25 35 44 46 31 26 36 39 33 62 53
Long ship 24 23 23 25 23 23 19 19 19 29 25 32 32 25 22 21
Integral 25 25 25 27 26 26 39 47 48 34 29 39 41 31
Shillelagh 26 26 26 28 24 24 34 39 40 30 28 34 34 26 50 44
Boat-tie 27 27 27 22 28 28 16 14 14 36 27 38 37 27 13 13
Snake 28 28 29 24 27 29 40 42 44 32 30 35 36 28 49 47
Big S 29 29 28 29 29 27 41 45 47 37 31 37 40 32 66 58
Bi-pond 30 30 30 30 30 30 18 18 18 40 33 40 45 34 24 22
Trans-boat with tail 31 33 32 32 31 32 49 54 56 41 32 41 42 29 63
Boat tie ship 32 35 34 33 33 34 46 49 51 42 35 48 48 37
Hat 33 34 33 34 34 33 54 57 58 35 35 29 33 36 33
Very long ship 34 37 37 35 37 38 29 25 28 44 38 46 50 41 34 31
Heavyweight spaceship[note 2] 35 40 40 38 52 62 46 42
Very long boat 36 38 38 36 36 36 50 53 55 43 37 44 47 38 60 59
Tub with tail 37 39 39 37 38 37 57 45 39 49 51 39
Table and table 38 27 41 24 27 40 31
Canoe 40 24 24 24 29 27
Bookends 53 18 16 19 19
Dead spark coil 39 32 17 15 17 20
Beehive at beehive 21 22 21 21 23
Tumbler 47 72
Octagon 2 35 30 19
Cis-mirrored R-bee 42 31 22 19 22 23
Spark coil 41 18 20 16 20
Up dove on dove 20 20 23 25
Up wing on wing 23 22 25 27
Bi-loaf 2 36 23 20 22 28 25
Pentadecathlon 52 35 16 18 15 18
Small lake 32 30
Lake 2 26
Inverted double claw 32 30 32 35 34
xs32_c8970798cz319e0e913 36
Figure eight 28 27 27 37 33
Double claw 31 28 29 38 30
Cis-mirrored long hook 33 28 35 40
Very long canoe 37 34 34 41 37
Long inverted double claw 33 29 33 42 36
Mirrored dock 57 38 30 26 43
Carrier bridge carrier 38 35 38 44 39
Unix 36 33 37 45 38
Cis-mirrored worm 39 31 38 46
xs56_wggc97079cggzraahy3haarzw116is0si611 47
xs32_g88m99m88gz122diid221 35
Loaf back tie loaf 47 43 31 48 42
Four boats 25
Long boat on long boat 42 38 41 51 41
xp2_8kihewehik8z8k44owo44k8zw121w121 40
Cloverleaf 52
Mazing 45 40 45 54 43
Elevener 56 43 46 50 56 45
Mango at mango 44 41 43 57 46
Long canoe 82 48 48 53 58 50
Krake 34 45 44 30 59
Cis-fuse with two tails 51 50 52 61 54
xs28_4s3qq3s4z11622611 51
xs18_c89n871z311 53 51 54 63 55
xs36_ca97079acz359e0e953 64
Trans-snake-tie 60 58 60 65 62
xs48_g08k97079k80gzd5l8gxg8l5dzx1470741 67
Test tube baby 40 49 35 52
xs40_8kihe0ehik8z4ai2s0s2ia4zx1x1 68
Extra long barge 59 37 57 75 65
Very long barge 61 61 49 69 61
Loaf siamese loaf 55 59 61 70 60
Bi-cap 43 43 71
Phoenix 1 31
Block and two tails 58 60 63 73 56
Cross 57
xs24_39u0u93z3210123 47 42 52 74
O quad-loaf 55 42
xs14_wggc871z6221 56 56 59 76 64
Rotated C 31
Bi-pentadecathlon 1 46
Washing machine 52
Clock 62 31
Shuriken 35
Sidewalk 36

Notes

  1. ↑ Blinkers are more common in even orthogonal symmetries because two gliders can collide to form an interchange.
  2. ↑ 2.0 2.1 2.2 2.3 Spaceships aren't actually less common in higher symmetries; they're just less likely to escape.
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