1. CSE325 Computer Science and Sculpture Prof. George Hart

2. Orderly Tangles One interesting transformation of a Platonic solid is to form an “orderly tangle” by rotating and translating the faces in a symmetric manner. This can provide the foundation for visually interesting sculptural forms.

3. Derivation from Regular Polyhedron Rotate facesSlide in or out

4. Regular Polylinks Symmetric linkages of regular polygons Alan Holden built models –Cardboard or dowels Holden wrote: –Shapes, Spaces and Symmetry,1971 –“Regular Polylinks”, 1980 –Orderly Tangles, 1983 Table of lengths 4 Triangles

5. Generates Template to Print and Cut 4 Triangles

6. Robert J. Lang

7. Rinus Roelofs

8. Carlo Sequin

9. Regular Polylinks 4 Triangles6 Squares Left and right hand forms

10. Paper or Wood Models 6 Squares

11. Solid Freeform Fabrication 6 Squares

12. Theo Geerinck

13. Rinus Roelofs

15. Regular Polylinks 6 Pentagons - size scaled

16. Square Cross Section 6 Pentagons

17. Rinus Roelofs

18. Paper or Wood Models

19. Charles Perry, sculptor 1976, 12 tons, 20’ edge3 nested copies

20. Regular Polylinks 12 Pentagons

21. Rinus Roelofs

22. Wooden Puzzles Taiwan –Teacher Lin –Sculptor Wu Square cross sections Simple lap joint No glue Trial and error to determine length 12 Pentagons

23. Second Puzzle from Lin and Wu 10 Triangles

24. Many Analogous Puzzles Possible Each regular polylink gives a puzzle Also can combine several together: –Different ones interweaved –Same one nested Need critical dimensions to cut lengths No closed-form formulas for lengths Wrote program to: –Determine dimensions –Output templates to print, cut, assemble –Output STL files for solid freeform fabrication

25. Carlo Sequin

26. Five rectangles — one axis of 5-fold symmetry

27. Software Demo Soon to be available on class website

28. Combinations 4 Triangles + 6 Squares

29. Combinations 12 Pentagons + 10 Triangles

30. Models Difficult for Dowels 30 Squares around icosahedral 2-fold axes

31. Other Polygon Forms 8 Triangles

32. Spiraling Polygons 10 layers, each 6 Squares

33. Charles Perry Eclipse, 1973, 35’ tall

34. Things too Complex to Make 10 Spirals connect opposite faces of icosahedron

35. Curved Components Central Inversion 4 Triangles20 Triangles