Solid Freeform Fabrication of Aesthetic Objects

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Solid Freeform Fabrication of Aesthetic Objects

• George W. Hart
• Stony Brook University
• Dept. Computer Science

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• Sculpture
• Mathematical Models
• Fractals
• Goldberg Polyhedra
• 4D Polytope Projections
• Historical Leonardo Models
• Orderly Tangles
• Puzzles
• Student Projects

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1. Sculpture
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72 Pencils
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Chronosynclastic Infundibulum
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Just Two Cavities
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Disk Combobulation
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The Plastic Tableware of Damocles
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Rainbow Bits
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Fire and Ice
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Id like to make one thing perfectly clear
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Battered Moonlight
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Yin and Yang
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Gazmogenesis
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Rorschachohedron
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Fat and Skinny
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Whoville
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Whoville -- detail
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Roads Untaken
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The Susurrus of the Sea
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Loopy
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Millennium Bookball
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Twisted Rivers, Knotted Sea
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Twisted Rivers, Knotted Sea
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Twisted Rivers -- reconstruction
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Twisted Rivers RP design
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Tangled Reindeer
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This End Up
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Knot Structured
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Nessie
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Quintessence of Hedgehog
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Bouquet
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Frabjous
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Salamanders
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SFF Model (2.5 inch diam.)
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Complete!
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People
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Snarl wood model, 14 inch
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Snarl SFF model, 1 inch
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Snarl SFF model, 2 inch
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Star Corona
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Compass Points
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Compass Points
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Cagework
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Aardvarks
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Spaghetti Code
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Rendering
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Rendering, along 5-fold axis
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Solid Freeform Fabrication Model
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Spaghetti Code
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Deep Structure
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Gonads of the Rich and Famous
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Gonads of the Rich and Famous-- design --
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Gonads of the Rich and Famous-- design --
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Untitled
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Untitled
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Untitled
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Untitled
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Untitled
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2. Mathematical Models
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Fractal Sierpinski Tetrahedron
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Connected Structure
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Snub Truncated Icosahedron
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Zonohedron-61
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4D Polytope Projection Models
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FDM Machine with 120-Cell Model
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120-Cell, before dissolving support
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120-Cell

• 120 cells, 720 faces, 1200 edges, 600
  vertices.
• Cell-first parallel projection,(shows less than
  half of the edges.)

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Five-Legged-Bee Hive
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120-Cell perspective projection
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(smallest ?) 120-Cell

• Wax model, made on Sanders machine

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120-Cell perspective projection
Selective laser sintering
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Truncated 120-Cell
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Truncated 120-Cell - Stereolithography
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Zometool Truncated 120-Cell
MathCamp 2000
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Ambo 600-Cell
Bridges Conference, 2001
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Ambo 120-Cell
Orthogonal projection Stereolithography Can do
with Zome
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48 Truncated Cubes
Poor FDM model
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Goldberg Polyhedra(Fullerenes)
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Buckyballs

• C60, form of carbon
• 1985 discovery
• 1996 Nobel Prize in chemistry
• By
• Richard Smalley (Rice Univ.)
• Robert Curl (Rice Univ.)
• Sir Harold Kroto

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Geodesic Dome from Icosahedron
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Dual Tessellations
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Triangular Subdivisions
Area x2 xt t2
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Goldberg Polyhedra
(2,0)
(2,1)
(3,0)
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Goldberg(2,2) Goldberg(4,1)
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Goldberg (3,3) Goldberg(6,0)
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Goldberg (7,3)
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Goldberg (7,3)
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(No Transcript)
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Ernst Haeckel
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Ernst Haeckel
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Artificial Radiolarian
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Goldberg (2,1)
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Goldberg (3,1)
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Goldberg (3,1)
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Metal Goldberg (8, 3)
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Nested Spheres
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Nested Balls
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Untitled (Abraham Sharp)
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Untitled (Abraham Sharp)
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3. Historical Models Leonardo / Pacioli
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Sphere Model from Euclid
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Leonardo Model
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Leonardo Model
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4. Orderly Tangles
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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
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Regular Polylinks
4 Triangles
6 Squares
Left and right hand forms
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Regular Polylinks
12 Pentagons
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Regular Polylinks
6 Pentagons - size scaled
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Derivation from Regular Polyhedron
Slide in or out
Rotate faces
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Wooden Puzzles

• Taiwan
• Teacher Lin
• Sculptor Wu
• Square cross sections
• Simple lap joint
• No glue
• Trial and error to determine length

12 Pentagons
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Second Puzzle from Lin and Wu
10 Triangles
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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

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Generates Template to Print and Cut
4 Triangles
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Paper or Wood Models
6 Squares
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Solid Freeform Fabrication
6 Squares
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Square Cross Section
6 Pentagons
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Paper or Wood Models
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Orderly Tangle Puzzle
aluminum 30 parts
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Selective Laser Sintering (SLS)
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Selective Laser Sintering
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Curved ComponentsCentral Inversion
4 Triangles
Inverted
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Curved ComponentsCentral Inversion
20 Triangles
Inverted
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SLS Models Inverted Tangles
4 triangles
5 tetrahedra
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Tangle Software

• Available free at
• http//www.georgehart.com

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5. Puzzles
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Sculpture Puzzles
aluminum 12 parts
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Sculpture Puzzles
SLS 3 inch
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30-Piece Puzzle
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6. Student Projects

• CSE391 Special Topics
• Algorithms for Solid Modeling

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Student Projects