Schatz Evertible (Invertible) Dodecahedron

Schatz Evertible (Invertible) Dodecahedron for Printing with TPU Flexible Filament.

Schatz's eversion (or inversion ) kinematics is a fascinating world of geometry, motion, and other mathematics. It is, however, pretty hard to comprehend without a physical model. Words are not adequate to address the structural transformations. Make one, close your eyes and feel the movement of forms, as suggested by Paul Schatz himself. So I will stop here.

Included are two STL files for printing using flexible filament. The big one (165mm) is based on a pentagon with face circumradius of 25mm. The small one (124mm) is scaled to 75% of the big one. Please note that when a STL file is scaled down uniformly; the joints will become thinner, becoming more flexible but less durable.

References

1. Schatz, P. (2013/1975). The study of rhythms and technology: The evertible cube | polysomatic form-finding (P. Carline, Trans.). Sugen: Niggli Verlag (Original work published 1975 in German).
2. Bu, L. (2023). The oloid and the evertible cube: 3D design and printing. In J. Holdener, E. Torrence, C. Fong & K. Seaton (Eds.), Proceedings of Bridges 2023: Mathematics, Art, Music, Architecture, Culture (pp. 417-420). Halifax, NS: Tessellations Publishing. https://archive.bridgesmathart.org/2023/bridges2023-417.html#gsc.tab=0