Transcript Orderly Tangles - George W. Hart

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 lengths
4 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 Components
Central Inversion
4 Triangles
20 Triangles