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.

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