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 facesSlide 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 Triangles6 Squares Left and right hand forms

Paper or Wood Models 6 Squares

Solid Freeform Fabrication 6 Squares

Theo Geerinck

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’ edge3 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

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 Triangles20 Triangles