Here are some 3-D models where all the coloured regions touch each other. They all have pleasing symmetry to my mind:

• torus with 7 colours.
• double torus with 8 colours.
• triple torus with 9 colours.
• triple torus with 9 colours flattened to a single sheet (so it could be made of paper.)

These use WebGL technology, and work on most modern platforms, including mobile phones. On a laptop/PC the mouse scroll wheel does scaling, and the Shift key allows rotation and scaling. On a mobile 2 fingertips will scale / rotate the image.

There's little connection with hexagons (yet) - just something of general interest.

page date: 12Oct16.      I enjoy correspondence stimulated by this site. You can contact me here.