Polygons of perimeters <= 8
made from uncrossed knight moves
Each knight move is represented by a straight line segment of scaled length 1,
which needs to be rotated and rescaled by Sqrt(5) to fit on a chessboard.
To enable the use of Markus Sigg's Snake Viewer program, the true
direction changes of the knight's path are rounded to the nearest integer
multiples of 9 degrees. The inexact graphical representation of the closed polygons
occasionally leads to open figures with potentially unidentified symmetry.
The direction changes of the path are coded by letters and 0:
0 (continuation of previous direction), d, D, f, F, j, J (right angle turn), n, N, p, P.
The diameter of the enclosing circle of the path calculated by the drawing program
usually deviates from the indicated exact diameter due to the said mapping of the angles.
Turning angle code, diameter of enclosing circle (symmetry)
Perimeter = 4 (3 polygons):
PDP, 1.8973665961 (symmetric)
JJJ, 1.4142135624 (symmetric)
FNF, 1.7888543820 (symmetric)
Perimeter = 6 (13 polygons):
PJ0NJ, 2.2360679775
PJfPJ, 2.4083189158 (symmetric)
PDJFN, 2.0000000000
PDFJJ, 2.4083189158
PD0PD, 2.8635642127 (symmetric)
P0N0P, 2.2360679775 (symmetric)
JJ0JJ, 2.2360679775 (symmetric)
JJdNF, 2.4083189158
JFJNn, 1.8027756377
JFJ0N, 2.2360679775
JFDJF, 2.4083189158 (symmetric)
JdNJd, 2.4083189158 (symmetric)
FN0FN, 2.7202941017 (symmetric)
Perimeter = 8 (178 polygons):
PJJDJPj, 1.9436506316
PJJ0JNd, 2.2360679775
PJJjNJF, 2.3177361425
PJJpPJJ, 2.0000000000 (symmetric)
PJDPpPJ, 2.0000000000
PJDJPpP, 1.9436506316
PJDJ0P0, 2.4037008503
PJDFJNj, 2.4083189158
PJD0P0J, 2.8635642127
PJDdNJ0, 2.8926366759
PJDjPJD, 2.6832815730 (symmetric)
PJ0NdNF, 2.4037008503
PJ0JNjP, 2.2360679775
PJ0JJNn, 2.2360679775
PJ0JDPf, 2.4037008503
PJ0JDJF, 2.4037008503
PJ0DJJ0, 2.8926366759
PJ00NJd, 3.1622776602
PJ00NFD, 3.1622776602
PJ0fPJ0, 3.1622776602 (symmetric)
PJfP0JJ, 2.4270609799
PJfPfPD, 2.5938388539
PJfJPjN, 2.6832815730 (symmetric)
PJfJFNd, 2.6832815730
PJfJFJD, 2.6832815730
PJfFN0J, 3.1622776602
PJfFJJ0, 3.1622776602
PJf0PDF, 3.4058772732
PJjNJ0P, 2.3177361425
PJjN0P0, 2.7648920592
PJjJNdN, 2.8284271247
PJjJJDJ, 2.8284271247
PJjDP0J, 3.2249030993
PJpPDJJ, 2.2803508502
PJpP0NF, 2.7202941017
PJpJPfP, 2.5298221281 (symmetric)
PJpJJFJ, 2.5385910353
PDJF0NF, 2.7202941017
PDJ0PfP, 2.4037008503
PDJ0JFJ, 2.4037008503
PDJ0FN0, 2.7479120088
PDJdJNd, 2.6832815730
PDJdJJD, 2.6832815730
PDJjPDJ, 2.8284271247 (symmetric)
PDJnNJF, 2.7283304386
PDFNnNJ, 2.4083189158
PDFJ0JJ, 2.4270609799
PDFJfPD, 2.6201729184
PDFDPjN, 2.6832815730 (symmetric)
PDFDFNd, 2.6832815730
PDFDFJD, 2.6832815730
PDF0NJj, 3.1622776602
PDF0N0J, 3.1622776602
PDF0JJ0, 3.1622776602
PDFfPDF, 3.4058772732 (symmetric)
PD0P0DP, 2.8811863126 (symmetric)
PD0PfJJ, 2.8635642127
PD0PjNF, 2.8990398640
PD0JJdN, 2.8926366759
PD0JFNj, 2.8926366759
PD0JFDJ, 2.8926366759
PD0FNdJ, 3.4058772732
PD0FJJf, 3.4058772732
PD0FJDF, 3.4058772732
PD00PD0, 3.8470768123 (symmetric)
PDdNJjP, 2.8635642127
PDdNF0N, 2.8990398640
PDdN0Pf, 2.9960526299
PDdN0JF, 2.9960526299
PDdJJ0J, 3.2249030993
PDdDP0D, 3.7947331922 (symmetric)
PDjP0N0, 3.0103986447
PDjJJFD, 3.2249030993
PDnNFJD, 2.8635642127
PDnJN0J, 2.8284271247
P0N0FJJ, 2.7202941017
P0NdN0P, 2.4037008503 (symmetric)
P0NjP0N, 2.6076809621 (symmetric)
P0NjJJF, 2.7648920592
P0NnNFJ, 2.5385910353
P0NnJN0, 3.0000000000
P0JNnJN, 2.3035022138
P0JJjNJ, 2.5000000000
P0JDJ0P, 2.4037008503 (symmetric)
P0JD0P0, 2.9960526299
P0J0NdN, 2.8284271247
P0J0JNj, 2.8284271247
P0J0JDJ, 2.8284271247
P0JfP0J, 3.2249030993 (symmetric)
P0JjNJ0, 3.1622776602
P0DJJjP, 2.8635642127
P0DJF0N, 2.8990398640
P0DJ0JF, 2.9960526299
P0DFJ0J, 3.2249030993
P0D0P0D, 3.7947331922 (symmetric)
P00NFfP, 3.0413812651
P00N0FJ, 3.0413812651
P00NdN0, 3.1622776602
P00JDJ0, 3.1622776602
PfPfPfP, 2.5298221281 (symmetric)
PfPfJFJ, 2.5938388539 (symmetric)
PfJJ0FN, 2.7283304386
PfJJdJJ, 2.6201729184 (symmetric)
PfJFDFJ, 2.6201729184 (symmetric)
PjNJdJN, 2.5385910353 (symmetric)
PjNFDFN, 2.5385910353 (symmetric)
pJJFDFJ, 2.5385910353 (symmetric)
JJFfJJF, 3.1622776602 (symmetric)
JJFjNFJ, 2.6832815730
JJFjJN0, 3.1622776602
JJ0J0JJ, 2.8284271247 (symmetric)
JJ0JdNF, 3.1622776602
JJ0FJNn, 2.7283304386
JJ0FJ0N, 2.7648920592
JJ0FDJF, 3.1622776602
JJ00JJ0, 3.1622776602 (symmetric)
JJ0dNJd, 3.2249030993
JJ0dNFD, 3.2249030993
JJdN0FN, 2.7479120088
JJdNdJJ, 2.6832815730 (symmetric)
JJdJN0n, 2.5385910353
JJdJNnN, 2.5385910353
JJdJDFJ, 2.6832815730
JJdJ0N0, 3.1622776602
JJdDJJd, 3.2249030993 (symmetric)
JJdDJFD, 3.2249030993
JJd0NF0, 3.4058772732
JJjJFJ0, 2.8926366759
JJjFN0F, 3.1622776602
JJnNJJn, 2.2803508502 (symmetric)
JJnNJdN, 2.4670670346
JJnNFDJ, 2.4670670346
JJnJNdJ, 2.6832815730
JJnJJDF, 2.6832815730 (symmetric)
JFNd0NJ, 2.8926366759
JFNjJFN, 2.6076809621 (symmetric)
JFJDdNJ, 2.8926366759
JFJ00NF, 3.1622776602
JFJfJFJ, 2.6832815730 (symmetric)
JFDJ0FN, 2.7479120088
JFDFN0n, 2.5385910353
JFDFNnN, 2.5385910353
JFDFDFJ, 2.6832815730 (symmetric)
JFDF0N0, 3.1622776602
JFD0JFD, 3.2249030993 (symmetric)
JFDdNF0, 3.4058772732
JF0JNdj, 2.7283304386
JF0JNnJ, 2.7283304386
JF0J0Nd, 2.9960526299
JF0J0JD, 2.9960526299
JF0DJF0, 3.4058772732 (symmetric)
JFjNJFj, 2.6832815730 (symmetric)
JFjNJdJ, 2.6832815730
JFjNFDF, 2.6832815730
J0J0J0J, 2.8284271247 (symmetric)
J0JdN0F, 3.1622776602
J0FNdNn, 2.7283304386
J0FNd0N, 2.9960526299
J0FDJ0F, 3.1622776602 (symmetric)
J0dNJ0d, 3.2249030993 (symmetric)
JdNJjFN, 3.1622776602
JdNFjNF, 2.6832815730
JdN0JdN, 3.1622776602 (symmetric)
JdNdNFj, 2.6832815730
JdNdNdJ, 2.6832815730 (symmetric)
JdNdJDF, 2.6832815730 (symmetric)
JdJDJdJ, 2.6832815730 (symmetric)
JdJDFDF, 2.6832815730 (symmetric)
Jd0NJd0, 3.4058772732 (symmetric)
Jd0NFDd, 3.4058772732
JnJNdNd, 2.6832815730 (symmetric)
FN0F0NF, 3.5777087640 (symmetric)
FN00FN0, 3.6878177829 (symmetric)
FNdDFNd, 3.4058772732 (symmetric)
FNnNF0N, 2.7578171722 (symmetric)
FDFDFDF, 2.6832815730 (symmetric)
F0N0F0N, 3.5777087640 (symmetric)
dNdNdNd, 2.6832815730 (symmetric)
Back to A323134