Möbius Polyhedral Model

This shape is a Möbius strip that is made out of triangles that form a sort of polyhedron. It's a bit tricky to figure out how to glue it together, but once you do, you can convince yourself that it really is a Möbius strip by tracing your finger along the faces and see that it has a surface with one side.

Steps

1. Cut out pattern.
   
2. Fold valley folds on the dashed lines and mountain folds along the dot-dashed lines.
   
3. Glue the tabs so the two sides labeled "A" line up and the two sides labeled "B" line up.
   
4. Make sure that the edge between the two A's is a valley fold and that the edge between the two B's is a mountain fold. This will start to twist the two halves in opposite directions.
   
5. Continue to twist until you can glue the tabs so sides labeled "C" line up and sides labeled "D" line up.
   
6. Glue the remaining tabs.
   

Notes

• This model was invented by Bryant Tuckerman, a pioneer in flexagons and inventor of the "Tuckerman's traverse," a way to reach all faces of a flexagon.
  

References

• (Gardner, The Scientific American Book of Mathematical Puzzles & Diversions 1959)