1 1/4 x 2 1/2 x 3/4" basswood
Drill and 1/2" bit
See the Wood Carving section for more instructions, hints and tips.
You may sometimes here a Mobius strip referred to as an endless ribbon.
It REALLY helps to have a 3-D model made from leather about 8" long and 3/8" wide. Leather works well because it is thick and flexible. Form a circle and then give one end a half twist. Glue the ends together and clamp until dry. It should easily form a figure 8.
Note in the photo above that there are three legs of the figure 8 that curve to the inside of the loop and one leg that curves to the outside of the loop. The odd outside loop is at the bottom left.
Start by drilling two holes 1/2" in diameter. Locate the center of these holes 5/8" from the top and bottom, leaving 1/4" of wood.
Cut the perimeter of the figure 8 out of the basswood block.
It might help to mark the odd leg for references purposes on both your model and project.
As you carve, watch the grain. You'll be cutting in all different directions, so just be careful. If the wood starts to splinter, work from the opposite direction or at a right angle to the direction of the split.
When you are carving, always strive for a band about 1/8" by 3/8" wide. Make the curves flow gently. Frequently refer to your model to help you visualize the final product.
Smooth out any irregularities and clean it up.
Now, do you have a mobius strip? Take a pencil and draw a centerline all the way around. If you made a true mobius strip, you can do it without lifting the pencil off the wood. You'll go all round on both sides and end up where you started. Well, except for the spot where they cross that you can't reach with the pencil.
Check out the page on topology for more information on mobius strips.
To make a really interesting carving (although more fragile), cut the band in half all the way around. If it is a mobius strip then it won't come apart because it has only one surface.
Photo coming soon.