Monohedron
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Monohedron: a square swept along a circle with a 90° twist -- one face, one edge, endless loop.
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- GNU General Public License v3.0
This model is a monohedron: a geometric solid with only one face and one edge, generated by sweeping a square along a circular path while rotating it 90° over a full 360° revolution.
Inspired by the Möbius strip but built with a quarter-turn twist on a square cross-section, it challenges classical polyhedron definitions ; four lateral faces merge seamlessly into a single continuous surface with no boundary. Trace the surface or follow the edge "with your finger", and you'll always return to your starting point without ever crossing a seam.
A fascinating object to hold, to study, and to explain to anyone who walks by your desk.
The photographs were taken with a monohedron printed using woodfill filaments.
The monohedron should be printed vertically to minimize the amount of support material needed. The STL and STEP files are already oriented accordingly. When using woodfill filaments, I found it necessary to lower the object by 0.2 mm to improve bed adhesion.
You must enable the experimental "Extra perimeters on overhangs" in the "Layers and Perimeters" settings.
Of course, feel free to try other orientations.