CSE 325 Computer Science and Sculpture Prof George

Orderly Tangles One interesting transformation of a Platonic solid is to form an “orderly

Derivation from Regular Polyhedron Rotate faces Slide in or out

Regular Polylinks • Symmetric linkages of regular polygons • Alan Holden built models –

Generates Template to Print and Cut 4 Triangles

Regular Polylinks 4 Triangles Left and right hand forms 6 Squares

Regular Polylinks 6 Pentagons - size scaled

Charles Perry, sculptor 1976, 12 tons, 20’ edge 3 nested copies

Wooden Puzzles • Taiwan – Teacher Lin – Sculptor Wu • Square cross sections

Second Puzzle from Lin and Wu 10 Triangles

Many Analogous Puzzles Possible • Each regular polylink gives a puzzle • Also can

Carlo Sequin Five rectangles — one axis of 5 -fold symmetry

Software Demo Soon to be available on class website

Combinations 12 Pentagons + 10 Triangles

Models Difficult for Dowels 30 Squares around icosahedral 2 -fold axes

Spiraling Polygons 10 layers, each 6 Squares

Things too Complex to Make 10 Spirals connect opposite faces of icosahedron

Curved Components Central Inversion 4 Triangles 20 Triangles

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CSE 325 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 Left and right hand forms 6 Squares

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’ 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-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