cse325 computer science and sculpture
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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. - PowerPoint PPT PresentationTRANSCRIPT
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.
Derivation from Regular Polyhedron
Rotate faces Slide in or out
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 lengths4 Triangles
Generates Template to Print and Cut
4 Triangles
Robert J. Lang
Rinus Roelofs
Carlo Sequin
Regular Polylinks
4 Triangles 6 Squares
Left and right hand forms
Paper or Wood Models
6 Squares
Solid Freeform Fabrication
6 Squares
Theo Geerinck
Rinus Roelofs
Rinus Roelofs
Regular Polylinks
6 Pentagons - size scaled
Square Cross Section
6 Pentagons
Rinus Roelofs
Paper or Wood Models
Charles Perry, sculptor
1976, 12 tons, 20’ edge 3 nested copies
Regular Polylinks
12 Pentagons
Rinus Roelofs
Wooden Puzzles
• Taiwan– Teacher Lin– Sculptor Wu
• Square cross sections• Simple lap joint• No glue• Trial and error to
determine length
12 Pentagons
Second Puzzle from Lin and Wu
10 Triangles
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
Carlo Sequin
Carlo Sequin
Five rectangles — one axis of 5-fold symmetry
Software Demo
Soon to be available on class website
Combinations
4 Triangles + 6 Squares
Combinations
12 Pentagons + 10 Triangles
Models Difficult for Dowels
30 Squares around icosahedral 2-fold axes
Other Polygon Forms
8 Triangles
Spiraling Polygons
10 layers, each 6 Squares
Charles Perry
Eclipse, 1973, 35’ tall
Things too Complex to Make
10 Spirals connect opposite faces of icosahedron
Curved ComponentsCentral Inversion
4 Triangles 20 Triangles