Use a paint program, such as Paint Shop Pro

Draw a hexagon to use as the basis of your tessellation.

It needn't be a regular hexagon, but make sure that you can draw a line between opposite corners of your hexagon that passes through the centre, and that opposite corners are the same distance from the centre (shown by the solid green line here). This makes sure it will tessellate.

Mark the corners of the hexagon and remove the sides.

Now draw a curve through four of the corners, replacing three sides of your previous hexagon.

Take a copy of one of the sides and paste it exactly onto the opposite side. The corners should line up.

Do the same with the next side.

And finally the last side.

If you found that there was an overlap when you pasted, you'll have to go back and redraw the first curve.

Now decorate your shape - here's one I did earlier....

It tessellates like this

If you start with a concave hexagon, and go wild with the curves, you might end up with something like this:

which tessellates, believe it or not:

page date: 23Oct05.      I enjoy correspondence stimulated by this site. You can contact me here.