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.
- Cut out pattern.
- Fold valley folds on the dashed lines and mountain folds along the dot-dashed lines.
- Glue the tabs so the two sides labeled "A" line up and the two sides labeled "B" line up.
- 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.
- Continue to twist until you can glue the tabs so sides labeled "C" line up and sides labeled "D" line up.
- Glue the remaining tabs.
- 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.