Stellation of Polyhedra and Organic Geometrical Sculpture
Vladimir Bulatov
Corvallis, Oregon, USA
http://bulatov.org
( PDF Version )
 Geometry  Polyhedra
 Polyhedra Stellation
 Stellation based wooden sculptures
 Making organic shapes  subdivision
 Technology
 Metal Sculpture
 Inspiration in Nature
Geometry  Polyhedra
No definition exists to satisfy everybody
Common property  simple and beautiful
Johnson's Solids
Polyhedra Stellation
Extension of polyhedron's faces to form new faces.
Stellation step 1
Stellation step 2
Stellation step 3
Stellation step 4
Stellation step 5
Stellation step 6
Stellation step 7
Stellation step 8
Stellation step 9
Stellation step 10
Stellation step 11
Stellation step 12
Stellations of RTC
Stellations of RTC
Stellations of RTC
Stellations of RTC
Stellations of RTC
Stellations of RTC
Stellations of RTC
Stellations of RTC
Stellations of RTC
Stellations of RTC
Stellations of RTC
Stellations of RTC
Stellations of RTC
Stellations of RTC
Stellations of RTC
Stellations of RTC
Stellations of RTC
Stellations of RTC
Wood. Stellation of Rhombic Triacontahedron
My first wood sculpture (2001) based on stellation of rhombic triacontahedron.
Stellation of Small Stellated Truncated Dodecahedron
Two kind of wood is used.
Stellation of Small Stellated Truncated Dodecahedron
Stellation of Small Stellated Truncated Dodecahedron
Stellation of Rhombic Triacontahedron
Stellation of Rhombic Triacontahedron
Stellation of Rhombic Triacontahedron
Stellation of Tetrakishexahedron
I don't like straight lines anymore and use curved inlays on flat faces.
Stellation of Tetrakishexahedron
Stellation of Tetrakishexahedron
Pentagonal Hexecontahedron
Curved inlays. Faces are sanded to rounded shape.
Small Stellated Dodecahedron
First sculpture with curved faces. Faces are 12 intersecting flat pentagrams.
Small Stellated Dodecahedron
Small Stellated Dodecahedron
Great Dodecahedron
Faces are 12 well rounded pentagons with cutouts.
Great Dodecahedron
Great Dodecahedron
Great Dodecahedron
Rhombic Triacontahedron
Faces are 30 rhombuses with deep curved cutouts.
Rhombic Triacontahedron
Rhombic Triacontahedron
Organic Shapes  Subdivision
How to transform set of flat polygons into an organic shape?
Subdivision example: Block
For each face, split each edge in half and move new vertices to make shape more rounded.
Subdivision. Step 1
Subdivision. Step 2
Subdivision. Step 3
Subdivision. Step 4
Subdivision example  Torus
Subdivision. Step 1
Subdivision. Step 2
Subdivision. Step 3
Subdivision. Step 4
Example 1
First Stellation of Icosahedron
Example 1
Select one face
Example 1
Make deep cuts
Example 1
Repeat for every face
Example 1
Add some thickness
Example 1
Subdivision step 1
Example 1
Subdivision step 2
Example 1
Subdivision step 3
Example 1
Add creases
Icosahedron I
Metal sculpture
Icosahedron I
Metal sculpture
Icosahedron I
Icosahedron I
Example 2
Great Dodecahedron
Example 2

Each pentagonal face is replaced with pentagon with deep cutouts 
Example 2
Subdivision step 1
Example 2
Subdivision step 2
Example 2
Subdivision step 3
Example 2
Subdivision step 4
Dodecahedron VI
Dodecahedron VI
Dodecahedron VI
Dodecahedron VI
Example 3
Rhombic Triacontahedron.
Example 3
First stellation of rhombic triacontahedron.
Example 3

Before Subdivision. Faces  30 rhombuses with deep cutouts.
 
Example 3
Subdivision. Step 1
Example 3
Subdivision step 2
Example 3
Subdivision step 3
Triacontahedron II
Triacontahedron II
Triacontahedron II
Example 4
Great Stellated Dodecahedron
Example 4
Before Subdivision
Example 4
Subdivision step 1
Example 4
Subdivision step 2
Example 4
Subdivision step 3
Dodecahedron X
Dodecahedron X
Dodecahedron I
Dodecahedron I
Dodecahedron I
Dodecahedron IX
Dodecahedron IX
Dodecahedron IX
Icosahedron II
Icosahedron II
Icosahedron II
Icosahedron III
Icosahedron III
Icosahedron III
Triacontahedron I
Triacontahedron I
Triacontahedron I
Triacontahedron III
Triacontahedron III
Triacontahedron III
Triacontahedron III
Dodecahedron II
Dodecahedron II
Dodecahedron II
Dodecahedron III
Dodecahedron III
Dodecahedron IV
Dodecahedron IV
Dodecahedron IV
Dodecahedron V
Dodecahedron V
Dodecahedron VII
Dodecahedron VII
Dodecahedron VIII
Dodecahedron VIII
Icosahedron VII
Great Icosahedron
Icosahedron VII
Great Icosahedron
Icosahedron VII
Great Icosahedron
What next?
Triacontahedron IV
Triacontahedron IV
Triacontahedron IV
Icosahedron IV
Icosahedron IV
Icosahedron IV
Icosahedron V
Icosahedron V
Icosahedron V
Five Tetrahedra
Five Tetrahedra
Five Tetrahedra
Rhombic Dodecahedron I
Rhombic Dodecahedron I
Rhombic Dodecahedron I
Dodecahedron XI
Dodecahedron XI
Dodecahedron XI
Dodecahedron XI
Dodecahedron XII
Dodecahedron XII
Dodecahedron XII
Origami I
Origami I
Origami I
Orthoplex I
Orthoplex I
Orthoplex I
Octaplex I
Octaplex I
Octaplex I
Octaplex II
Octaplex II
Octaplex II
Hyperbolic I
Projects
Projects
Projects
Projects
Projects
Projects
Projects
Projects
Inspiration in Nature  Ernst Haeckel
Are my shapes organic? I hope so.
Here are few examples from the book
Ernst Haeckel "Art Forms In Nature".
Ernst Haeckel  Art Forms In Nature
Ernst Haeckel  Art Forms In Nature
Ernst Haeckel  Art Forms In Nature
Ernst Haeckel  Art Forms In Nature
Ernst Haeckel  Art Forms In Nature
Ernst Haeckel  Art Forms In Nature
Ernst Haeckel  Art Forms In Nature
Ernst Haeckel  Art Forms In Nature
Ernst Haeckel  Art Forms In Nature
Ernst Haeckel  Art Forms In Nature
Ernst Haeckel  Art Forms In Nature