List of common objects by symmetry

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 regards every census as 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^{[note 3]}	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
Mirrored table	38									27	41	24	27	40	31
Canoe	40						24	24	24						29	27
Cis-mirrored bookend	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 bun	42		31							22		19	22		23
Spark coil			41								18		20	16		20
Cis-mirrored dove										20		20	23		25
Cis-mirrored 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 bookend										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
Mirrored cap												43	43		71
Phoenix 1						31
Block on cover							58	60	63						73	56
Cross																57
Mirrored very long house										47		42	52		74
O quad-loaf								55	42
xs14_wggc871z6221							56	56	59						76	64
Rotated house		31
Bi-pentadecathlon 1													46
Washing machine								52
Clock	62			31
Shuriken					35
Sidewalk			36

Notes

↑ Blinkers are more common in even orthogonal symmetries because two gliders can collide to form an interchange.
↑ ^2.0 ^2.1 ^2.2 ^2.3 Spaceships aren't actually less common in higher symmetries; they're just less likely to escape.
↑ Integrals are more common near the edge of a soup. They only appear to be rarer in symmetric soups because the soup size is larger.

[1] Blinkers are more common in even orthogonal symmetries because two gliders can collide to form an interchange.

[spaceship-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.

[3] Integrals are more common near the edge of a soup. They only appear to be rarer in symmetric soups because the soup size is larger.

[note 1]

[note 2]

[note 3]

List of common objects by symmetry

Notes

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