Knight's Tours Geometry Classes

31 Geometrically Distinct Closed Knight's Tours

Here is the breakdown of the number of Geometrically Distinct Closed Knight's Tours, or "Geometry Classes" as coined by George P. Jelliss.

There are five sections that contain all 31 Geometry Classes.  These classes reflect the Knight's Tours that are unique tours.  Unique tours simply means that the tours are not reflections, rotations, or reversals of another Knight's Tour.

Section 1 has 16 Geometry Classes.  Though there are 17 Knight's Tours in this section, two of the tours have the same geometric pattern, or Geometry Class.  Therefore, there are only 16 Geometrically Distinct Tours in this section.  Section 2 = 1 Geometry Class, Section 3 = 7 Geometry Classes, Section 4 = 6 Geometry Classes, and Section 5 = 1 Geometry Class.

Check out the following tours that represent all 31 separate Geometry Classes out of the 63 Closed Knight's Tours.

Section 1 = 16 Geometry Classes

Section-1, Geometry Class-1

Section-1, Geometry Class-2

Section-1, Geometry Class-3

Section-1, Geometry Class-4

Section-1, Geometry Class-5

Section-1, Geometry Class-6

Section-1, Geometry Class-7

Section-1, Geometry Class-8

Section-1, Geometry Class-9

Section-1, Geometry Class-10

Section-1, Geometry Class-11

Section-1, Geometry Class-12

Section-1, Geometry Class-13

Section-1, Geometry Class-14

Section-1, Geometry Class-15

Section-1, Geometry Class-16

Section 2 = 1 Geometry Class

Section-2, Geometry Class-1

Section 3 = 7 Geometry Classes

Section-3, Geometry Class-1

Section-3, Geometry Class-2

Section-3, Geometry Class-3

Section-3, Geometry Class-4

Section-3, Geometry Class-5

Section-3, Geometry Class-6

Section-3, Geometry Class-7

Section 4 - 6 Geometry Classes

Section-4, Geometry Class-1

Section-4, Geometry Class-2

Section-4, Geometry Class-3

Section-4, Geometry Class-4

Section-4, Geometry Class-5

Section-4, Geometry Class-6

Section 5 = 1 Geometry Class

Section-5, Geometry Class-1