Self-avoiding polygons of perimeters <= 11
on hexagonal lattice

Hugo Pfoertner, 2018-06-27

OEIS A284869, A316196 (symmetric polygons)

Code list of turning angles in degrees (12-gonal encoding):
0(0), -60(b), +60(B), -120(d), +120(D),

Turning angle code, diameter of enclosing circle (symmetry)

Perimeter = 3:
DD, 1.1547005384 (mirror,rot3)

Perimeter = 4:
BDB, 1.7320508076 (mirror,rot2)

Perimeter = 5:
0DBB, 2.0000000000 (mirror)

Perimeter = 6:
0BD0B, 2.6457513111 (rot2)
0D0D0, 2.3094010768 (mirror,rot3)
bDBBB, 2.0000000000 (mirror)
BBBBB, 2.0000000000 (mirror,rot6)

Perimeter = 7 (5 polygons, 3 symmetric):
00DB0B, 3.0000000000 (mirror)
0BBBB0, 2.6943012562 (mirror)
0BBDbB, 2.6943012562
0BDbD0, 2.6457513111
BBBBDd, 2.0000000000 (mirror)

Perimeter = 8 (16 polygons, 10 symmetric):
00BD00B, 3.6055512755 (rot2)
00D0BB0, 3.0550504633 (mirror)
00D0DbB, 3.0550504633
0bDBB0B, 3.0000000000
0B0D0B0, 3.4641016151 (mirror,rot2)
0B0DBbB, 3.4641016151 (mirror)
0BBB0BB, 3.0000000000 (mirror,rot2)
0BBB0Db, 2.8000000000 (mirror)
0BBBBbD, 3.0000000000
0BBBDdB, 2.6943012562
0BBDdD0, 2.6943012562
0BDdDB0, 2.6943012562 (mirror)
0BDbBDb, 2.8000000000
0BDbDbD, 3.0000000000 (mirror)
0DbD0Db, 2.6457513111 (mirror,rot2)
bDBBbDB, 3.0000000000 (point)

Perimeter = 9 (37 polygons, 9 symmetric):
000DB00B, 4.0000000000 (mirror)
00BBB0B0, 3.6055512755
00BBBBbB, 3.6055512755
00BBDb0B, 3.6055512755
00BDbBB0, 3.6055512755
00BDbDbB, 3.6055512755
00BD0bD0, 3.6055512755
00DbD0B0, 3.4641016151
00DbDBbB, 3.4641016151
00D00D00, 3.4641016151 (mirror,rot3)
00D0BDdB, 3.0550504633
00D0DdD0, 3.0550504633 (mirror)
0bDBBbD0, 3.0550504633
0bDB0DbB, 3.0550504633
0bDB0BB0, 3.0550504633
0bBD0B0B, 3.6055512755
0BbDB0B0, 3.6055512755
0BbDBBbB, 3.6055512755
0B0D0DdB, 3.4641016151
0BB0BB0B, 3.0550504633 (mirror)
0BB0BBBb, 3.0550504633
0BB0DbDb, 3.0550504633 (mirror)
0BB0DBdB, 3.0550504633 (mirror)
0BBBbDBb, 3.0550504633
0BBB0BDd, 3.0000000000
0BBBBdDB, 3.0000000000
0BBBDd0D, 3.0000000000
0BBDdBDb, 2.8000000000
0BBDdDbD, 3.0000000000
0BBDbbDB, 3.0000000000 (mirror)
0BDdD0Db, 2.8000000000
0BDdDBbD, 3.0000000000
0BDbBBDd, 3.0000000000
0DbBBBBb, 3.0550504633 (mirror)
0DbBDbDb, 3.0550504633
bDBBdDBB, 3.0000000000
bDBbDBbD, 3.0550504633 (rot3)

Perimeter = 10 (120 polygons, 36 symmetric):
000BD000B, (rot2)
000D0B0B0, (mirror)
000D0BBbB,
000D0Db0B,
000DBbDbB, (mirror)
00bDBB00B,
00B0D00B0, (rot2)
00B0D0BbB,
00B0DBb0B,
00BB0BB00, (mirror)
00BB0DbB0,
00BB0D0bB,
00BBBbD00,
00BBB00BB, (mirror,rot2)
00BBB00Db, (mirror)
00BBB0BbD,
00BBB0DdB,
00BBBBdD0,
00BBBBb0D,
00BBBDd0B,
00BBDdBB0,
00BBDdDbB,
00BBDbbD0,
00BDdD0B0,
00BDdDBbB,
00BDb0D00,
00BDbB0Db,
00BDbBBbD, (mirror)
00BDbBDdB,
00BDbDdD0,
00BDbDb0D,
00BD0dDB0,
00BD0bBDb,
00DdDB0B0,
00DdDBBbB,
00DbBDbB0,
00DbBD0bB,
00DbDbD00, (mirror)
00DbD00Db, (mirror,rot2)
00DbD0DdB,
00DbDBdD0,
00D00DBdB, (mirror)
0bDBB0bDB, (rot2)
0bDBBbDbD,
0bDBBbBDb,
0bDBBbBBB,
0bDBBdDB0,
0bDB0Db0D,
0bDB0DdD0,
0bDB0BDdB,
0bDB0BBbD,
0bDB0B0Db,
0bDB0B0BB,
0bDBbDBbB,
0bDBbD0B0,
0bD0D0bD0, (rot2)
0bD0DbDbB,
0bD0DbBB0,
0bD0BBBbB,
0bD0BB0B0,
0BdDBB0B0,
0BdDBBBbB,
0bBD0BbD0,
0bBBDbB0B,
0BbBD0BbB, (rot2)
0BbD0DbB0, (mirror)
0BbDB0BbD, (rot2)
0BbDB0DdB,
0BbDBBdD0,
0b0DB0B0B, (mirror)
0B0BB0B0B, (mirror,rot2)
0B0BB0BBb,
0B0BBBbBB, (mirror)
0B0BBBbDb,
0B0BBBBdB,
0B0BBDbbB,
0B0BDbBbD, (mirror)
0B0BDbDdB,
0B0BD0dD0,
0B0DbBBBb, (mirror)
0B0DbDbDb, (mirror)
0B0DbDBdB,
0BBbD0BBb, (rot2)
0BBbDBbBB,
0BBbDBbDb,
0BBbDBBdB,
0BB0BB0Dd, (mirror)
0BB0BBBdD,
0BB0BBDd0,
0BB0BDdDb,
0BB0BDbbD, (mirror)
0BB0BD0dB,
0BB0DdDBb,
0BBBdDBBb,
0BBBbD0Dd,
0BBBbDBdD,
0BBBDdbDB,
0BBDd0DBb,
0BBDdBBDd,
0BBDdBDdD,
0BBDdDdDB, (mirror)
0BDdBBBBb,
0BDdBDbDb,
0BDdDbDBb,
0BDdD0BDd, (rot2)
0BDdD0DdD, (mirror)
0BDbbDBBb,
0dDBBBbD0,
0DdD0DbDb, (mirror)
0DdDBbDBb,
0DbBBDdDb,
0DbBDdDBb, (mirror)
bDBBbBBDb, (mirror)
bDBbDBdDB,
bDBbDbDBb, (rot2)
bDBbBDbDb, (mirror)
bDBbBDbBB, (mirror)
bDBbBBBBb,
BdDBBBdDB, (rot2)
bBBBBbBBB, (mirror,rot2)

Perimeter = 11 (344 polygons, 27 symmetric, only symmetric polygons shown):
0000DB000B, (mirror)
000D00BB00, (mirror)
000D0DbbD0, (mirror)
00B0BB0B00, (mirror)
00BB0B0B0B, (mirror)
00BBBbDbBB, (mirror)
00BBBBdBBB, (mirror)
00BBDb0bDB, (mirror)
00BDbbDB00, (mirror)
00BDb0D0bD, (mirror)
00BDbDdDbD, (mirror)
00DbBB0BBb, (mirror)
00DbDbDbDb, (mirror)
00DbDBdBDb, (mirror)
00D0bD0Db0, (mirror)
0BbBBBBbB0, (mirror)
0B0B0DbBBb, (mirror)
0B0B0DBbbB, (mirror)
0B0BB0B0Dd, (mirror)
0BB0BDdDdD, (mirror)
0BB0BD0d0D, (mirror)
0BB0DdD0Dd, (mirror)
0BDdBBBBdD, (mirror)
0BDbbDB0Dd, (mirror)
bDBBdBBDbB, (mirror)
bDBbDbBDbB, (mirror)
bBDdDBbBBB, (mirror)

Back to A284869, back to A316196