A Smörgåsbord of Skyrmions: index, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16
15a ε1.0932 ± 0.0001
b0.9999
r3.2074
VD(3180.0,21397.4,21404.2)
UD(569.3,552.0,552.4)
0.52%symC1h
A 7a-Skyrmion attached to a 8a-Skyrmion.
15b ε1.0937 ± 0.0001
b0.9999
r2.5832
VD(6189.2,10165.7,13009.2)
UD(547.3,574.0,560.9)
6.38%symC2v
A 7a-Skyrmion attached to two cubes. Like the triangular 12h-Skyrmion but with one cube replaced with a dodecahedron.
15c ε1.0938 ± 0.0001
b0.9999
r2.5729
VD(5803.6,10279.8,13196.0)
UD(551.9,563.9,559.8)
17.6%sym∅ [R. Battye and P. Sutcliffe, Phys. Rev. C73, 055205 (2006)]
Out-of-phase graphene.
15d ε1.0938 ± 0.0001
b0.9999
r2.7947
VD(4235.7,14768.8,15650.4)
UD(544.4,554.3,554.7)
15.2%symC1h
Part of a 10a-Skyrmion attached to a 7a-Skyrmion.
15e ε1.0938 ± 0.0001
b0.9999
r2.7984
VD(4230.6,14830.4,15683.3)
UD(544.4,554.0,555.6)
8.57%sym
A 7a-Skyrmion attached to symmetric graphene.
15f ε1.0939 ± 0.0001
b0.9999
r2.5937
VD(5446.0,10917.0,13399.9)
UD(573.4,552.3,545.5)
0.02%symC1h
Symmetric graphene.
15g ε1.0940 ± 0.0001
b0.9999
r2.5268
VD(6029.7,9481.9,12542.7)
UD(579.0,562.7,543.1)
5.19%sym
Out-of-phase graphene.
15h ε1.0942 ± 0.0001
b0.9999
r2.5317
VD(7660.0,7981.4,12694.1)
UD(607.3,548.8,544.3)
2.93%symC1h
The triangular 12h-Skyrmion with a tetrahedron added at one edge center.
15i ε1.0942 ± 0.0001
b0.9999
r2.5417
VD(6568.0,9082.2,12936.4)
UD(602.9,542.6,546.8)
7.21%symC1h
Symmetric graphene.
15j ε1.0942 ± 0.0001
b0.9999
r2.8117
VD(5391.6,13773.2,15931.8)
UD(579.3,554.8,547.6)
0.13%symC1h
A 7a-Skyrmion attached to a 8a-Skyrmion.
15k ε1.0943 ± 0.0001
b0.9999
r2.6061
VD(5280.5,11251.5,13478.8)
UD(575.4,549.8,545.7)
0.06%symC1h
Symmetric graphene.
15l ε1.0944 ± 0.0001
b0.9999
r2.5639
VD(6455.9,9457.8,13152.1)
UD(611.0,541.5,540.0)
5.59%symC1h
Symmetric graphene.
15m ε1.0944 ± 0.0001
b0.9999
r2.8406
VD(3948.3,15449.4,16539.0)
UD(572.4,549.9,549.3)
3.16%symC1h
A cube attached to symmetric graphene. Analogous to the 12e-Skyrmion.
15n ε1.0944 ± 0.0001
b0.9999
r2.5656
VD(6472.1,9482.6,13149.7)
UD(603.5,541.8,546.6)
0.17%symC1h
Similar to the 15l-Skyrmion but with a different reflection symmetry. Can also be interpreted as a 5a-Skyrmion attached to the chain 10c-Skyrmion.
15o ε1.0944 ± 0.0001
b0.9999
r2.5807
VD(5931.2,10240.0,13269.4)
UD(581.4,545.2,553.1)
0.06%symC1h
Symmetric graphene.
15p ε1.0945 ± 0.0001
b0.9999
r2.9186
VD(4009.3,16662.7,17180.7)
UD(557.4,547.5,550.6)
0.11%symC2v
Two 7a-Skyrmions joined by a single Skyrmion.
15q ε1.0945 ± 0.0001
b0.9999
r2.9024
VD(4162.0,16486.6,16735.1)
UD(546.0,559.1,554.1)
0.31%symC2v
Two 7a-Skyrmions joined by a single Skyrmion.
15r ε1.0945 ± 0.0001
b0.9999
r2.9099
VD(4110.0,16562.9,16921.1)
UD(546.1,555.3,556.9)
0.09%symC1h
Two 7a-Skyrmions joined by a single Skyrmion, preserving only a reflection related the two dodecahedra.
15s ε1.0945 ± 0.0001
b0.9999
r2.6417
VD(5490.3,11428.8,14022.1)
UD(549.8,560.9,563.7)
1.29%symC1h
Symmetric graphene.
15t ε1.0946 ± 0.0001
b0.9999
r2.7146
VD(4463.6,13724.9,14371.8)
UD(546.4,554.7,557.1)
0.64%symC1h
Two 7a-Skyrmions joined by a single Skyrmion, preserving only a reflection related the two dodecahedra.
15u ε1.0946 ± 0.0001
b0.9999
r2.8881
VD(4107.4,16236.0,16772.8)
UD(539.0,556.2,549.7)
0.42%sym
A 7a-Skyrmion attached to a 8b-Skyrmion through a face.
15v ε1.0946 ± 0.0001
b0.9999
r2.7879
VD(4289.3,14673.5,15548.2)
UD(539.9,550.4,562.1)
0.07%symC1h
A 7a-Skyrmion loosely attached to symmetric graphene.
15w ε1.0947 ± 0.0001
b0.9999
r2.6246
VD(6393.7,10246.7,13933.1)
UD(590.2,545.9,557.5)
6.49%symC1h
Symmetric graphene.
15x ε1.0947 ± 0.0001
b0.9999
r2.5346
VD(6402.5,9196.6,12808.1)
UD(585.0,556.4,544.1)
0.02%sym
Asymmetric graphene.
15y ε1.0949 ± 0.0001
b0.9999
r2.9175
VD(4214.8,16409.7,17320.3)
UD(569.7,543.3,545.2)
0.33%symC1h
A 7a-Skyrmion attached to a 8c-Skyrmion.
15z ε1.0949 ± 0.0001
b0.9999
r2.9745
VD(4998.3,16155.2,18396.9)
UD(584.2,549.8,557.1)
0.74%symC2v
Two cubes attached to a A 7a-Skyrmion, to form a hinge.
15aa ε1.0949 ± 0.0001
b0.9999
r2.7060
VD(5226.9,12446.9,14897.5)
UD(568.8,556.5,553.1)
5.08%sym
Asymmetric graphene.
15ab ε1.0950 ± 0.0001
b0.9999
r2.7705
VD(4314.7,14189.1,15694.8)
UD(578.4,544.7,552.9)
1.03%sym
Symmetric graphene attached to a cube, without preserving a reflection symmetry.
15ac ε1.0950 ± 0.0001
b0.9999
r2.7862
VD(4249.5,14475.3,15858.3)
UD(543.3,567.8,565.2)
0.46%symC1h
Symmetric graphene attached to a cube, preserving a reflection symmetry.
15ad ε1.0950 ± 0.0001
b0.9999
r2.8269
VD(4117.1,15124.0,16383.1)
UD(541.5,558.9,573.8)
0.02%symC1h
Symmetric graphene attached to a cube, without preserving a reflection symmetry.
15ae ε1.0951 ± 0.0001
b0.9999
r2.5597
VD(5773.6,10086.5,13179.2)
UD(586.0,554.4,548.9)
0.42%sym
Out-of-phase graphene attached to a cube.
15af ε1.0951 ± 0.0001
b0.9999
r2.7977
VD(4031.9,14808.9,16043.2)
UD(541.5,569.9,561.5)
0.09%symC1h
Symmetric graphene attached to a cube.
15ag ε1.0952 ± 0.0001
b0.9999
r3.0900
VD(4099.7,18598.3,20040.0)
UD(550.5,567.6,577.3)
0.44%symC1h
A long chain with a tetrahedron acting as a hinge. An extension of the 11i-Skyrmion.
15ah ε1.0952 ± 0.0001
b0.9999
r2.6232
VD(6168.2,10461.4,13911.9)
UD(543.7,582.2,566.4)
0.09%sym
A 13f-Skyrmion with a 2-torus attached.
15ai ε1.0952 ± 0.0001
b0.9999
r2.7667
VD(4543.1,13888.5,15656.3)
UD(548.0,561.3,567.1)
0.06%symC1h
Symmetric graphene attached to a cube.
15aj ε1.0952 ± 0.0001
b0.9999
r2.7344
VD(4398.5,13619.1,15300.4)
UD(543.2,560.5,557.5)
2.45%sym
Asymmetric graphene.
15ak ε1.0954 ± 0.0001
b0.9999
r2.8213
VD(5028.6,14143.5,16321.9)
UD(543.8,553.6,586.0)
2.06%symC1h
Symmetric graphene, featuring a distinct 6a-Skyrmion.
15al ε1.0955 ± 0.0001
b0.9999
r3.1689
VD(4186.5,19590.6,21216.1)
UD(557.3,564.4,576.5)
0.04%symC1h
A long chain with a 5a-Skyrmion as a hinge.
15am ε1.0955 ± 0.0001
b0.9999
r2.5145
VD(7202.2,8135.9,12761.3)
UD(550.1,569.8,560.2)
0.02%symC1h
Symmetric graphene.
15an ε1.0956 ± 0.0001
b0.9999
r2.6405
VD(4807.2,12246.8,13994.2)
UD(546.2,551.2,558.7)
1.27%sym
Asymmetric graphene.
15ao ε1.0956 ± 0.0001
b0.9999
r3.0381
VD(3678.0,18315.4,19310.1)
UD(578.2,545.4,551.1)
1.12%sym
An 8b-Skyrmion joined to a 8a-Skyrmion, sharing a single Skyrmion.
15ap ε1.0956 ± 0.0001
b0.9999
r2.5224
VD(7233.5,8248.9,12808.1)
UD(569.8,555.0,556.6)
0.06%sym
Asymmetric graphene.
15aq ε1.0956 ± 0.0001
b0.9999
r2.8132
VD(4787.7,14445.4,16072.1)
UD(547.4,565.9,559.8)
0.20%symC1h
The 11d-Skyrmion attached to a cube.
15ar ε1.0957 ± 0.0001
b0.9999
r2.9604
VD(3978.4,17015.8,18198.6)
UD(546.4,558.5,571.1)
0.04%symC1h
A deformed 10a-Skyrmion attached to a 5a-Skyrmion.
15as ε1.0957 ± 0.0001
b0.9999
r2.5218
VD(7707.8,7712.0,12980.3)
UD(559.3,557.4,557.6)
0.09%symC3v
A triangular fullerene. Could also be interpreted as out-of-phase graphene.
15at ε1.0957 ± 0.0001
b0.9999
r2.8158
VD(4858.9,14322.9,16201.3)
UD(580.2,545.1,552.7)
0.07%symC1h
Similar to the 15aq-Skyrmion but the cube is rotated by 45°.
15au ε1.0957 ± 0.0001
b0.9999
r2.5338
VD(6827.2,8963.1,12751.0)
UD(579.9,547.6,559.3)
6.33%sym
Deformed symmetric graphene. In the terminology of ref.Manton:2011mi,Feist:2012ps, this is a flat square with one corner cut off.
15av ε1.0958 ± 0.0001
b0.9999
r2.4927
VD(6609.7,8612.1,12262.2)
UD(574.8,554.9,551.7)
0.04%sym
Asymmetric graphene.
15aw ε1.0958 ± 0.0001
b0.9999
r2.8004
VD(4854.9,14975.3,15016.3)
UD(540.5,549.4,554.4)
0.13%symC1h
A 8b-Skyrmion loosely attached to a 7a-Skyrmion.
15ax ε1.0959 ± 0.0001
b0.9999
r2.6522
VD(4707.9,12389.1,14262.6)
UD(561.8,549.1,551.4)
0.02%symC1h
Symmetric graphene.
15ay ε1.0960 ± 0.0001
b0.9999
r2.7173
VD(4628.0,13970.2,14288.5)
UD(547.1,560.2,556.2)
0.13%symC1h
The 13a-Skyrmion with a 2-torus attached.
15az ε1.0961 ± 0.0001
b0.9999
r2.6120
VD(5358.3,11262.0,13689.4)
UD(590.1,551.3,537.3)
0.02%symC1h
Symmetric graphene.
15ba ε1.0961 ± 0.0001
b0.9999
r2.5300
VD(7890.4,7957.1,12637.4)
UD(575.7,552.0,562.2)
0.35%sym
Two cubes joined by a single Skyrmion, attached to a 6a-Skyrmion.
15bb ε1.0962 ± 0.0001
b0.9999
r2.6286
VD(5150.5,11608.0,14033.9)
UD(541.1,550.4,582.1)
0.52%symC2
Almost-symmetric graphene.
15bc ε1.0962 ± 0.0001
b0.9999
r2.9501
VD(3776.5,17007.5,18216.9)
UD(550.1,564.5,574.3)
0.09%sym
Symmetric graphene attached to a 6a-Skyrmion.
15bd ε1.0963 ± 0.0001
b0.9999
r2.6967
VD(5652.2,11988.3,14731.3)
UD(576.8,560.6,551.7)
0.02%sym
Out-of-phase graphene attached to a 5a-Skyrmion.
15be ε1.0963 ± 0.0001
b0.9999
r2.6583
VD(5054.3,12204.3,14222.5)
UD(580.6,552.5,544.7)
0.02%sym
Almost-symmetric graphene.
15bf ε1.0964 ± 0.0001
b0.9999
r2.6851
VD(4955.0,12798.5,14260.3)
UD(578.9,549.6,550.7)
0.06%sym
A 7a-Skyrmion attached to a 8d-Skyrmion.
15bg ε1.0965 ± 0.0001
b0.9999
r2.9294
VD(4160.3,16333.6,17935.1)
UD(571.6,564.0,550.8)
0.04%sym
Symmetric graphene attached to a 6a-Skyrmion.
15bh ε1.0966 ± 0.0001
b0.9999
r2.8619
VD(4551.6,15180.5,16835.1)
UD(550.1,571.1,584.0)
0.18%sym
Four clusters: three cubes and one tetrahedron, in a chain.
15bi ε1.0967 ± 0.0001
b0.9999
r2.6224
VD(6070.8,10565.1,14023.0)
UD(542.4,574.0,565.1)
0.07%sym
A 10a-Skyrmion attached to a 5a-Skyrmion, forming almost-symmetric graphene.
15bj ε1.0967 ± 0.0001
b0.9999
r2.6567
VD(5200.7,11870.6,14267.9)
UD(561.6,568.9,566.6)
0.09%symC1h
Symmetric graphene attached to a cube.
15bk ε1.0968 ± 0.0001
b0.9999
r2.6678
VD(4759.6,12407.8,14618.2)
UD(549.8,567.1,556.2)
0.15%sym
Symmetric graphene attached to a tetrahedron.
15bl ε1.0968 ± 0.0001
b0.9999
r2.7182
VD(9003.0,9099.4,14791.8)
UD(554.0,580.8,581.3)
0.29%symC3v
Three cubes attached symmetrically by a tetrahedral hinge.
15bm ε1.0969 ± 0.0001
b0.9999
r2.6630
VD(4959.7,12187.6,14418.9)
UD(596.9,541.9,546.3)
0.02%symC2v
Symmetric graphene.
15bn ε1.0970 ± 0.0001
b0.9999
r2.5733
VD(6861.1,9571.7,12950.7)
UD(555.0,567.8,580.3)
0.09%symC1h
Two cubes joined by single Skyrmion, attached to a 6a-Skyrmion. Analogous to the 13d-Skyrmion.
15bo ε1.0971 ± 0.0001
b0.9999
r2.9722
VD(5033.1,16065.8,18468.3)
UD(588.0,564.8,553.7)
0.02%sym
The bent chain 12i-Skyrmion, with a tetrahedron attached.
15bp ε1.0971 ± 0.0001
b0.9999
r3.0818
VD(4625.6,17951.6,20062.8)
UD(583.5,551.6,567.6)
0.02%symC1h
A long chain. Can be thought of as the 12i-Skyrmion bent chain with an added 2-torus on one end and a single Skyrmion on the other.
15bq ε1.0972 ± 0.0001
b0.9999
r2.9383
VD(4420.1,16271.9,17981.4)
UD(581.5,560.4,546.3)
0.02%symC1h
Symmetric graphene with two distinct cubes at the ends.
15br ε1.0972 ± 0.0001
b0.9999
r2.5492
VD(6211.7,9811.1,12898.7)
UD(590.9,552.9,547.1)
0.02%symC2
Two 6a-Skyrmions attached by a tetrahedron.
15bs ε1.0972 ± 0.0001
b0.9999
r2.9533
VD(3764.1,17085.4,18271.1)
UD(583.9,565.9,547.8)
0.02%sym
Extended symmetric graphene.
15bt ε1.0973 ± 0.0001
b0.9999
r2.9094
VD(4910.2,15987.0,16941.2)
UD(582.7,554.8,558.4)
0.04%sym
The 11i-Skyrmion with an edge 2-torus replaced by a 6a-Skyrmion.
15bu ε1.0973 ± 0.0001
b0.9999
r2.6357
VD(6546.9,11205.2,13103.3)
UD(587.4,565.1,555.4)
0.22%sym
A 8a-Skyrmion joined to an 8-Skyrmion formed of two cubes in the same orientation, sharing a 1-Skyrmion.
15bv ε1.0974 ± 0.0001
b0.9999
r2.9566
VD(4377.5,16556.7,18204.7)
UD(580.1,557.2,556.9)
0.04%symC1h
Long symmetric graphene.
15bw ε1.0974 ± 0.0001
b0.9999
r2.5852
VD(5590.1,10932.7,13159.0)
UD(578.6,542.9,552.6)
0.31%sym
Almost-symmetric graphene.
15bx ε1.0976 ± 0.0001
b0.9999
r3.2271
VD(3393.8,21462.3,21985.3)
UD(583.2,563.8,551.0)
0.02%sym
A chain comprised of the 6a-Skyrmion and the 9d-Skyrmion.
15by ε1.0978 ± 0.0001
b0.9999
r2.4061
VD(5475.9,9930.8,10042.3)
UD(562.0,566.2,567.8)
0.02%symC1h
Two shells surround a single Skyrmion, with a single reflection symmetry.
15bz ε1.0978 ± 0.0001
b0.9999
r2.4527
VD(5398.8,10289.9,10811.7)
UD(577.7,561.4,558.4)
0.06%sym
Part of a 9b-Skyrmion attached to a long chain.
15ca ε1.0979 ± 0.0001
b0.9999
r2.3988
VD(6436.4,8433.8,10464.6)
UD(577.6,564.4,558.1)
0.07%sym
A conglomerate of Skyrmion clusters.
15cb ε1.0979 ± 0.0001
b0.9999
r2.7361
VD(5028.5,13198.5,15250.6)
UD(543.5,579.0,563.8)
0.06%sym
A 5a-Skyrmion attached to symmetric graphene.
15cc ε1.0979 ± 0.0001
b0.9999
r2.4460
VD(6227.5,8936.4,11185.2)
UD(571.2,568.8,563.2)
0.02%symC1h
A conglomerate of Skyrmion clusters, with a reflection symmetry.
15cd ε1.0979 ± 0.0001
b0.9999
r3.0182
VD(3827.2,18273.3,18740.4)
UD(573.3,559.1,558.5)
0.02%sym
A 6a-Skyrmion loosely attached to a 9a-Skyrmion.
15ce ε1.0980 ± 0.0001
b0.9999
r2.3906
VD(6801.3,8190.4,10121.9)
UD(593.2,556.3,561.6)
0.22%sym
A conglomerate of Skyrmion clusters.
15cf ε1.0980 ± 0.0001
b0.9999
r2.6283
VD(5408.4,11386.5,13986.8)
UD(600.6,542.7,552.5)
0.06%symD2h
Symmetric graphene.
15cg ε1.0984 ± 0.0001
b0.9999
r2.4674
VD(6033.4,10199.1,10683.4)
UD(549.2,565.3,579.8)
0.06%symC1h
Two 6a-Skyrmions joined by a 5a-Skyrmion.
15ch ε1.0986 ± 0.0001
b0.9999
r2.8124
VD(4571.3,15252.2,15513.8)
UD(568.8,548.5,553.3)
0.02%sym
A 6a-Skyrmion attached to a 9b-Skyrmion.
15ci ε1.0986 ± 0.0001
b0.9999
r2.3213
VD(6569.4,7627.9,9086.2)
UD(549.3,606.9,583.3)
0.13%symC1h
Three cubes with a 2-torus and a single Skyrmion attached.
15cj ε1.0989 ± 0.0001
b0.9999
r2.3221
VD(7013.6,7025.8,9243.7)
UD(583.5,577.5,577.7)
0.02%symC3v
A flat structure with three distinct single Skyrmions and three distinct 2-tori.
15ck ε1.0989 ± 0.0001
b0.9999
r2.3194
VD(6612.6,7438.0,9170.4)
UD(586.8,579.2,573.4)
0.04%sym
A conglomerate of Skyrmion clusters with a 2-torus in the center.
15cl ε1.0991 ± 0.0001
b0.9999
r2.4290
VD(5575.5,9491.4,10604.5)
UD(556.4,572.1,585.9)
0.02%sym
A conglomerate of Skyrmion clusters. There is a definite 8b-Skyrmion cluster and a 2-torus in the center.
15cm ε1.0998 ± 0.0001
b0.9999
r2.3361
VD(5864.0,8579.3,9151.8)
UD(560.1,589.2,591.4)
0.02%symC1h
A flat structure, with a 2-torus attached.
15cn ε1.1007 ± 0.0001
b0.9999
r2.3494
VD(7450.3,8089.8,8673.7)
UD(556.6,593.0,576.4)
0.02%sym
A conglomerate of Skyrmion clusters.