graphic with four colored squares

Stellation of Polyhedra and Organic Geometrical Sculpture

Vladimir Bulatov
Corvallis, Oregon, USA
http://bulatov.org

( PDF Version )

Geometry - Polyhedra

No definition exists to satisfy everybody

Common property - simple and beautiful

5 Platonic solids

Faces - identical regular convex polygons, transitive under transformations of a symmetry group.
Convex.

4 Kepler-Poinsot solids

Faces - identical regular (possible non-convex) polygons, transitive under transformations of a symmetry group

13 Arhimedean Solids

Faces are regular convex polygons, transitive under transformations of symmetry group.
Truncated Tetrahedron
Cuboctahedron
Truncated octahedron
Truncated cube
Rhombicuboctahedron
Truncated cuboctahedron
Snub cube
Icosidodecahedron
Truncated icosahedron
Truncated dodecahedron
Rhombicosidodecahedron
Truncated icosidodechedon
Snub dodecahedron

53 Uniform Polyhedra

Faces are regular polygons. Transitive under transformations of a symmetry group

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


End

For more info visit: http://bulatov.org