A 9x12 Tour and a Group of 10x11 Tours

 The following 9x12 tour was constructed quickly as a sort of doodle. 

9x12

This design was the basis for the following tours of the 10x11 board, showing the different types of symmetry possible on this board. The Bergholtian tour was the first constructed. The others were derived from this by simple transformations. 

 

10x11 Open

10x11 Eulerian

10x11 Bergholtian

10x11 Axial

The Bergholtian tour passes twice through the centre. The Eulerian tour circles round the centre. The Open tour passes once through the centre. These three all have 180 degree rotational symmetry.