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CSE325 Computer Science and Sculpture

CSE325 Computer Science and Sculpture. Prof. George Hart. 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.

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CSE325 Computer Science and Sculpture

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  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 faces Slide 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 Triangles 6 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

  14. 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’ edge 3 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. Carlo Sequin 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 ComponentsCentral Inversion 4 Triangles 20 Triangles

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