Self-avoiding polygons of perimeters <= 8
with turning angles from regular 12-gon
Code list of turning angles in degrees:
0(0), +-30(Aa), +-60(Bb), +-90(Cc), +-120(Dd), +-150(Ee)
Turning angle code, diameter of enclosing circle (symmetry)
Perimeter = 3 (1 symmetric polygon):
DD, 1.1547005384 (mirror,rot3)
Perimeter = 4 (3 symmetric polygons):
AEA, 1.9318516526 (mirror,rot2)
BDB, 1.7320508076 (mirror,rot2)
CCC, 1.4142135624 (mirror,rot4)
Perimeter = 5 (4 polygons, 3 symmetric):
0DBB, 2.0000000000 (mirror)
aEAC, 2.0000000000
ACCA, 2.0000000000 (mirror)
CCEd, 1.4142135624 (mirror)
Perimeter = 6 (22 polygons, 17 symmetric):
0AE0A, 2.9093129112 (rot2)
0BD0B, 2.6457513111 (rot2)
0CC0C, 2.2360679775 (mirror,rot2)
0D0D0, 2.3094010768 (mirror,rot3)
aEBaE, 2.7320508076 (rot2)
aEAAD, 2.7320508076
aEaEa, 2.2307101433 (mirror,rot3)
aEaDA, 2.2307101433 (mirror)
aDCaD, 2.3941701710 (rot2)
aDBAC, 2.3941701710
aDACA, 2.2307101433 (mirror)
AADAA, 2.7320508076 (mirror,rot2)
ABCAB, 2.3941701710 (rot2)
ABCCb, 2.3941701710
ACACA, 2.2307101433 (mirror)
ACBDc, 2.0000000000
ACDcD, 2.0000000000 (mirror)
ACEdC, 2.0000000000
ADAEd, 2.0000000000 (mirror)
bECbE, 2.3941701710 (rot2)
bDBBB, 2.0000000000 (mirror)
BBBBB, 2.0000000000 (mirror,rot6)
Perimeter = 7 (69 polygons, 13 symmetric):
00DB0B, 3.0000000000 (mirror)
0aEBaC, 2.9093129112
0aEAAB, 2.9093129112
0aDC0A, 2.9532542189
0ACBAA, 2.9093129112
0ACBBa, 2.9093129112
0ACCaB, 2.9093129112
0ACDbA, 2.9093129112
0ADA0C, 2.9532542189 (mirror)
0AEbCA, 2.9093129112
0AEbDa, 2.9093129112
0AEaAC, 2.9532542189
0BBBB0, 2.6943012562 (mirror)
0BBDbB, 2.6943012562
0BDbD0, 2.6457513111
0CABBA, 2.4786273499 (mirror)
0CABCa, 2.4786273499
0CADbC, 2.4786273499
0CAEcB, 2.4786273499
0CCbEa, 2.4786273499
0CC0Ed, 2.2360679775 (mirror)
0CCBdE, 2.2360679775
0CCEeA, 2.2360679775
0CEbbE, 2.2360679775 (mirror)
0dECBA, 2.3941701710
0DcEAA, 2.7320508076
0DcEBa, 2.7320508076
0DaCCa, 2.4786273499 (mirror)
aEBACE, 2.3941701710
aEBcDC, 2.7320508076
aEABAE, 2.7320508076 (mirror)
aEAaDB, 2.9093129112
aEAbEA, 2.7320508076
aEaEcD, 2.3941701710
aEaDaD, 2.7320508076
aEaCAC, 2.7320508076
aEcDBA, 2.3941701710
aEdEAB, 2.3941701710
aDCaBD, 2.9093129112
aDCbCC, 2.7320508076
aDCcDB, 2.3984791179
aDCdEA, 2.2307101433
aDBCdE, 2.3941701710
aDBAAD, 2.9093129112
aDBaDA, 2.7320508076
aDADcD, 2.3941701710
aDABAC, 2.7320508076
aDAADa, 2.7320508076 (mirror)
aDAACA, 2.7320508076
AdECAB, 2.3941701710
AbEABA, 2.7320508076
AbECbC, 2.7320508076
AACABA, 2.7320508076 (mirror)
AACCbC, 2.7320508076 (mirror)
AACDcB, 2.7320508076
AADCdC, 2.7320508076 (mirror)
ABBDcC, 2.3984791179
ABCADd, 2.3941701710
ABCCdD, 2.3941701710
ABDcDA, 2.3941701710
ABEdCB, 2.3941701710
ABEdEb, 2.3941701710
ACACCd, 2.2307101433
ACBBDe, 2.0000000000
ACBDeD, 2.0000000000
ADdECb, 2.3941701710
bECdDC, 2.3941701710
BBBBDd, 2.0000000000 (mirror)
BDcECd, 2.0000000000
Perimeter = 8 (418 polygons, 109 symmetric):
00AE00A, 3.8982242653 (rot2)
00BD00B, 3.6055512755 (rot2)
00CC00C, 3.1622776602 (mirror,rot2)
00D0BB0, 3.0550504633 (mirror)
00D0DbB, 3.0550504633
0aEB0aE, 3.6326508809 (rot2)
0aEBaAD, 3.6326508809
0aEBcEa, 2.9264631404
0aEBcDA, 2.9264631404
0aEAA0D, 3.6326508809
0aEAaD0, 3.0980762114
0aE0DcC, 2.9145489947
0aE0AC0, 3.0980762114
0aEaEbA, 3.0119423583
0aEaDaB, 3.0119423583
0aEaCBa, 3.0119423583
0aEaCAA, 3.0119423583
0aDC0aD, 3.2348263655 (rot2)
0aDCaAC, 3.2348263655
0aDCbDa, 2.9532542189
0aDCbCA, 2.9532542189
0aDBA0C, 3.2348263655
0aDADbA, 3.0119423583
0aDACaB, 3.0119423583
0aDABBa, 3.0119423583
0aDABAA, 3.0119423583
0aCD0aC, 3.3858679264 (rot2)
0aCDaAB, 3.3858679264
0aCCA0B, 3.3858679264
0aBEaAA, 3.7320508076
0aBDA0A, 3.7320508076
0A0E0A0, 3.8637033052 (mirror,rot2)
0A0EAaA, 3.8637033052 (mirror)
0AAD0AA, 3.6326508809 (rot2)
0AAD0Ba, 3.6326508809
0AADAaB, 3.6326508809
0AADBbA, 3.6326508809
0ABC0AB, 3.2348263655 (rot2)
0ABC0Cb, 3.2348263655
0ABCAaC, 3.2348263655
0ABCCcA, 3.2348263655
0AC0CA0, 3.0980762114 (mirror)
0AC0DaA, 3.0980762114
0ACAABA, 3.0119423583
0ACAACa, 3.0119423583
0ACACbC, 2.9532542189
0ACADcB, 2.9264631404
0ACBaCA, 3.0119423583
0ACBaDa, 3.0119423583
0ACB0AC, 3.3858679264 (rot2)
0ACB0Dc, 2.9168017012
0ACBAaD, 3.3858679264
0ACBBcD, 2.9532542189
0ACBCdC, 2.9093129112
0ACBDdA, 2.9093129112
0ACCcD0, 2.9145489947
0ACDdCA, 2.9093129112
0ACDdDa, 2.9093129112
0ACDcAC, 2.9532542189
0ACDbaD, 2.9532542189
0ACEdAB, 2.9093129112
0ACEcaC, 2.9093129112
0ADaBBA, 3.0119423583
0ADaBCa, 3.0119423583
0ADaDbC, 2.9532542189
0ADaEcB, 2.9264631404
0ADAbDA, 3.0119423583
0ADAbEa, 3.0119423583
0ADA0AD, 3.7320508076 (mirror,rot2)
0ADA0Ed, 2.9532542189 (mirror)
0ADAAaE, 3.7320508076
0ADABdE, 2.9532542189
0ADAEeA, 2.9093129112
0ADCdBC, 2.9532542189
0ADCbbE, 2.9532542189
0AEeEA0, 2.9208942636 (mirror)
0AEdDAA, 2.9093129112
0AEdDBa, 2.9093129112
0AEdEaB, 2.9093129112
0AEcCAB, 2.9532542189
0AEcCCb, 2.9093129112
0AEcDaC, 2.9532542189
0AEbACA, 3.0119423583
0AEbADa, 3.0119423583
0AEbBAC, 3.3858679264
0AEbBDc, 2.9168017012
0AEbCaD, 3.3858679264
0AEbDcD, 2.9532542189
0AEbEdC, 2.9093129112
0AEaaDA, 3.0119423583
0AEaaEa, 3.0119423583
0AEaAEd, 2.9532542189
0AEaBaE, 3.7320508076 (mirror)
0AEaCdE, 2.9532542189
0AE0dEA, 2.9093129112
0AE0cDB, 2.9532542189
0AE0bCC, 3.3858679264
0bEC0bE, 3.1196235041 (rot2)
0bECbBC, 3.1196235041
0bEAB0C, 3.1196235041
0bDBB0B, 3.0000000000
0bCEbBA, 3.3858679264
0BaE0Ba, 3.6326508809 (rot2)
0BaEAaB, 3.6326508809
0BaEBbA, 3.6326508809
0B0D0B0, 3.4641016151 (mirror,rot2)
0B0DBbB, 3.4641016151 (mirror)
0BAC0BA, 3.1196235041 (rot2)
0BAC0Ca, 3.1196235041
0BACBbC, 3.1196235041
0BACCcB, 3.1196235041
0BBB0BB, 3.0000000000 (mirror,rot2)
0BBB0Db, 2.8000000000 (mirror)
0BBBBbD, 3.0000000000
0BBBDdB, 2.6943012562
0BBDdD0, 2.6943012562
0BCAEeB, 2.6457513111
0BDeEAA, 2.7320508076
0BDeEBa, 2.7320508076
0BDdDB0, 2.6943012562 (mirror)
0BDcCBA, 2.7005792287
0BDcCCa, 2.7005792287
0BDcEbC, 2.6613478601
0BDbBDb, 2.8000000000
0BDbDbD, 3.0000000000 (mirror)
0BDaAEc, 2.9168017012
0BD0cEA, 2.7005792287
0BEaeEB, 2.6457513111
0cDCBaC, 2.9093129112
0cDCAAB, 2.9093129112
0CdEBAA, 2.9093129112
0CdEBBa, 2.9093129112
0CdECaB, 2.9093129112
0CbE0Cb, 3.2348263655 (rot2)
0CbEAaC, 3.2348263655
0CbECcA, 3.2348263655
0CaD0Ca, 3.1196235041 (rot2)
0CaDBbC, 3.1196235041
0CaDCcB, 3.1196235041
0C0C0C0, 2.8284271247 (mirror,rot4)
0C0CCcC, 2.8284271247 (mirror)
0CABADc, 2.7320508076
0CABBCd, 2.4786273499
0CABDdC, 2.4786273499
0CABEdA, 2.4786273499
0CABEca, 2.4786273499
0CACaEc, 2.7320508076
0CACDeB, 2.4786273499
0CADdDA, 2.4786273499 (mirror)
0CADdEa, 2.4786273499
0CADbEd, 2.4786273499
0CAD0dE, 2.4786273499
0CADCeA, 2.4786273499
0CAEeD0, 2.4786273499
0CBAEeC, 2.4037008503
0CCeECb, 2.4037008503
0CCdDCa, 2.4786273499
0CCbCDc, 2.7320508076
0CCbDCd, 2.4786273499
0CCAACE, 2.7320508076
0CCDdbE, 2.2360679775
0CCEeaD, 2.2360679775
0CDcBEc, 2.7320508076
0CDaBCE, 2.7320508076
0CEd0Ea, 2.4786273499
0CEdBEd, 2.2360679775
0CEdDdE, 2.2360679775 (mirror)
0DeDCAA, 2.7320508076
0DeDCBa, 2.7320508076
0dCDABA, 2.7320508076
0DcCDaA, 2.9145489947
0DcDACa, 2.7320508076
0DcEaDa, 2.7320508076
0DcE0Dc, 2.7320508076 (rot2)
0DcECdC, 2.7320508076
0DbD0Db, 2.6457513111 (mirror,rot2)
0DaADAa, 3.0980762114 (mirror)
0DaCBCd, 2.4786273499
0DaCEdA, 2.4786273499
0DaCEca, 2.4786273499
0DaEdEa, 2.4786273499 (mirror)
0DaEbEd, 2.4786273499
0DBcECd, 2.4786273499
0EdE0Ed, 2.2360679775 (mirror,rot2)
aEBACCD, 2.3941701710
aEBAADC, 2.9093129112
aEBAbEC, 3.3460652150
aEBaDAE, 2.7320508076
aEBaCBD, 2.9093129112
aEBaBCC, 3.3460652150
aEBcBEa, 3.3460652150 (mirror)
aEBcBDA, 3.3460652150
aEBdCEb, 2.9093129112
aEBdCCB, 2.9093129112
aEBeDBC, 2.7320508076
aEABACD, 2.7320508076
aEABaDC, 3.3460652150
aEABdEC, 2.9532542189
aEAACAE, 2.7320508076
aEAABBD, 2.9093129112
aEAAACC, 3.3460652150
aEAAaEA, 3.7320508076 (rot2)
aEAbECd, 2.7320508076
aEAbEaD, 3.0119423583
aEAbDAC, 3.0119423583
aEAbCDa, 3.3460652150
aEAbCCA, 3.3460652150
aEAcDBB, 2.9093129112
aEAdEAC, 2.7320508076
aEAdDCA, 2.7320508076
aEaEcBD, 2.9264631404
aEaEdCC, 2.7320508076
aEaEeDB, 2.3984791179
aEaDbCC, 2.9532542189
aEaDcDB, 2.9093129112
aEaDdEA, 2.7320508076
aEaCDeD, 2.4082836639 (mirror)
aEaCCdE, 2.7320508076
aEaCaEa, 3.3460652150 (mirror,rot2)
aEaCaDA, 3.3460652150
aEaBDcD, 2.8284271247 (mirror)
aEaBCaD, 3.0119423583
aEaBBAC, 3.0119423583
aEaBACA, 3.3460652150 (mirror)
aEbDBcE, 2.7645495854
aEbDaEb, 2.9093129112 (rot2)
aEbDaCB, 2.9093129112
aEbCEdB, 2.4786273499
aEbCCbD, 2.7645495854
aEbCADb, 2.9093129112
aEbCABB, 2.9093129112
aEcEAbE, 2.8284271247
aEcEaEc, 2.3941701710 (mirror,rot2)
aEcEaBC, 2.8284271247 (mirror)
aEcDCcD, 2.4437845714
aEcDBaD, 2.8284271247
aEcDADc, 2.3941701710 (mirror)
aEcDAAC, 2.8284271247
aEdCDaB, 2.7320508076
aEdCCAA, 2.7320508076
aEeDBBA, 2.3984791179
AeECABB, 2.3984791179
AeECADb, 2.3149479149
AeECCbD, 2.3984791179
aDCaCAE, 2.7320508076
aDCaBBD, 2.9093129112
aDCbEdE, 2.7320508076
aDCbCEd, 2.7320508076
aDCbADA, 3.3460652150
aDCdDAC, 2.7320508076
aDCdCDa, 2.7320508076 (mirror)
aDCdCCA, 2.7320508076
aDCeDBB, 2.3984791179
aDBEdbE, 2.3941701710
aDBCbCE, 2.7320508076
aDBCdCD, 2.9093129112
aDBBACE, 2.3984791179
aDBBcDC, 2.9532542189
aDBABAE, 2.7320508076
aDBAABD, 2.9093129112 (mirror)
aDBAaDB, 3.3858679264 (rot2)
aDBAbEA, 3.3460652150
aDBaDaD, 3.0119423583
aDBaCDc, 2.9093129112
aDBaCAC, 3.0119423583
aDBaBDa, 3.3460652150 (mirror)
aDBaBCA, 3.3460652150
aDBcDCa, 2.7320508076
aDBcDBA, 2.7320508076
aDBdEAB, 2.4786273499
aDAEdAD, 2.7320508076
aDADcBD, 2.9264631404
aDADdCC, 2.7320508076
aDADeDB, 2.3984791179
aDACbCC, 2.9532542189
aDACcDB, 2.9093129112
aDACdEA, 2.7320508076
aDABDeD, 2.4082836639
aDABCdE, 2.7320508076
aDABAEd, 2.7320508076
aDABaDA, 3.3460652150 (rot2)
aDAAEdC, 2.7320508076
aDAADcD, 2.8284271247
aDAACaD, 3.0119423583
aDAABDc, 2.9093129112
aDAABAC, 3.0119423583
aDAAADa, 3.3460652150 (mirror)
aDAAACA, 3.3460652150
aDaDaDa, 2.7320508076 (mirror,rot4)
aDaDaCA, 2.7320508076 (mirror)
aDaCCbC, 2.7320508076 (mirror)
aDaCABA, 2.7320508076 (mirror)
aDbEAbD, 2.9093129112
aDbDBaC, 2.9093129112
aDbDAAB, 2.9093129112
AdCDAAB, 2.9093129112
AdDCABA, 2.7320508076
AdDCCbC, 2.7320508076
AdEACAA, 2.7320508076
AdEBDcC, 2.3984791179
aCDbDcE, 2.9093129112
aCDbACB, 2.9093129112
aCDcEcD, 2.4786273499 (mirror)
aCDcCAC, 2.9093129112
aCDcBCA, 2.7320508076
aCCAaCC, 3.2348263655 (rot2)
aCCAbDB, 2.9093129112
aCCAcEA, 2.7320508076
aCCaBBB, 2.9093129112 (mirror)
aCCbEbC, 2.6165734602 (mirror)
aCCbCBA, 2.7320508076
aCBDcAD, 2.9093129112
aCBBBcE, 2.9093129112
aCBBaCB, 2.9093129112 (rot2)
aCBACbD, 2.9093129112
aCBAABB, 2.9093129112
aCACaCA, 2.7320508076 (mirror,rot2)
aCABABA, 2.7320508076 (mirror)
AcDBBAA, 2.9093129112
AcEABAB, 2.7320508076
AcEABCb, 2.6165734602
AcECbCB, 2.7320508076
AcECbEb, 2.5680646642
AcECAcE, 2.7320508076 (rot2)
aBEbCbE, 3.3460652150 (mirror)
aBEbABC, 3.3460652150
aBDAaBD, 3.6326508809 (rot2)
aBDAbCC, 3.3460652150
aBCBaBC, 3.3460652150 (mirror,rot2)
aBCAAAC, 3.3460652150 (mirror)
AbCCAAA, 3.3460652150
AbCDAbC, 3.3460652150 (rot2)
AbCEbAB, 3.3460652150
AbDBAAB, 2.9093129112
AbDBACb, 2.9093129112
AbDCAbD, 2.9093129112 (rot2)
AbEAAAC, 3.3460652150
AbEAADc, 2.8284271247
AbEACcD, 2.9093129112
AbEADdC, 2.7320508076
AbEBAbE, 3.3460652150 (rot2)
AbECdDA, 2.7320508076
AAACAAA, 3.3460652150 (mirror,rot2)
AAADBcB, 3.3460652150 (mirror)
AAAEbCb, 3.3460652150 (mirror)
AABBAAB, 2.9093129112 (mirror,rot2)
AABBACb, 2.9093129112
AABBBBc, 2.9093129112
AABCCdB, 2.9093129112
AABDcCA, 2.9093129112
AABDbDc, 2.9093129112
AACAADc, 2.8284271247 (mirror)
AACABCd, 2.7320508076
AACADdC, 2.7320508076
AACBDeB, 2.7320508076
AACCbEd, 2.7320508076
AADbCCb, 2.7645495854 (mirror)
AADbDBc, 2.7645495854
ABbEABb, 3.3858679264 (rot2)
ABABABA, 2.7320508076 (mirror,rot4)
ABABCbC, 2.7320508076 (mirror)
ABABDcB, 2.7320508076
ABACACd, 2.7320508076
ABACCdC, 2.7320508076 (mirror)
ABAEcDc, 2.7320508076 (mirror)
ABBACBd, 2.4786273499
ABBAEbb, 2.4786273499 (mirror)
ABBBDeC, 2.3984791179
ABBDeDA, 2.3984791179
ABBDcEd, 2.3984791179
ABCbEbC, 2.6165734602 (mirror)
ABCCeCC, 2.4786273499 (mirror)
ABCDccE, 2.3941701710
ABCEdbD, 2.3941701710
ABDeDBA, 2.4082836639 (mirror)
ABDcCDc, 2.4437845714
ABDcDCd, 2.3941701710
ABDcEcD, 2.4786273499 (mirror)
ABEdCDd, 2.3941701710
ABEdEdD, 2.3941701710
ABEcDeE, 2.3941701710
ABEbdEB, 2.3941701710
ACdECbC, 2.7320508076
ACcEACc, 2.9093129112 (rot2)
ACbDACb, 2.9093129112 (rot2)
ACbDBBc, 2.9093129112
ACbECdB, 2.9093129112
ACACEdb, 2.2307101433
ACAEdEd, 2.2307101433 (mirror)
ACBdECb, 2.4786273499
ACCdECd, 2.2307101433
ACDdCEd, 2.3941701710
ADdEADd, 2.3941701710 (rot2)
ADcDADc, 2.3941701710 (mirror,rot2)
ADcDBCd, 2.3941701710
ADbCCBd, 2.4786273499
ADbCEbb, 2.4786273499
bECeCEb, 2.4494897428 (mirror)
bECeCCB, 2.4786273499
bEbEbEb, 2.4494897428 (mirror,rot4)
bEbEbCB, 2.5680646642 (mirror)
bDBBbDB, 3.0000000000 (rot2)
BdECBdE, 2.2360679775 (rot2)
bCEcDcE, 2.7320508076 (mirror)
bCCBbCC, 3.1196235041 (rot2)
bCCBcDB, 2.7320508076
bCBCbCB, 2.7320508076 (mirror,rot2)
BcDCBcD, 2.7320508076 (rot2)
BcEBBcE, 2.9093129112 (rot2)
BBBBEcc, 2.0000000000 (mirror)
BBCdECc, 2.3984791179
BBDeECd, 2.0000000000
BCdEBCd, 2.3941701710 (rot2)
BCcDBCc, 2.5035872648 (rot2)
BDeDCCd, 2.0000000000
BDeEBDe, 1.9318516526 (rot2)
CeECCeE, 1.8803984644 (rot2)
CdDCCdD, 2.3941701710 (rot2)
Back to A316192