Abstract creations by Vladimir Bulatov

Vladimir Bulatov creates very complex and wonderful abstract bronze sculptures. Shapes of sculptures are based on Platonic solids, but they represent another view on these classic polyhedrons. All figures were designed using classical ideas of balance and symmetry. These abstract forms express geometric aesthetic and beauty of shapes.

The photo above shows five interconnected tetrahedrons, so they are look like a single complex closed shape. Other figures by Vladimir Bulatov are based on single Platonic shape, e.g. dodecahedron or icosahedron. or more complex Archimedian solid.

Dodecahedron IX (Small Stellated Dodecahedron)

Dodecahedron VII (Great Dodecahedron)

Dodecahedron VII (Great Dodecahedron)

Rhombic Triacontahedron IV

Visit his site http://bulatov.org to see more wonderful sculptures or, maybe, to buy them.

Kaleidocycles

Kaleidocycle consists of at least 6 tetrahedrons joined into chain, which head connected to it's tail. In the case of at least 8 tetrahedra it has the interesting property that it can be turned through its center in a continuous motion.

In the book "M.C.Escher kaleidocycles" (1977) the mathematician Doris Schattschneider and the graphic designer Wallace Walker showed how to cover kaleidocycles continuously with repeating patterns designed by Dutch artist M.C. Escher. It should be noted that in the work of Escher himself kaleidocycles do not appear.

Below you can see two examples of kaleidocycles decorated with Escher's tessellations.

The most comprehensive site about kaleidocycles is http://www.kaleidocycles.de/

Rapid prototyping sculptures

George Hart is active using rapid prototyping (RP) technology for modeling sculptures.

Rapid Prototyping or Solid Freeform Fabrication refers to a range of new technologies which construct physical three-dimensional objects by assembling thin layers of material under computer control. Objects can be made which are extremely accurate, complex, and beautiful, and which no other technology can produce.

The image left shows he and his model of Sierpinski triangle.

He also interested in four-dimensional geometry. From a 4D object, one can calculate 3D "shadows" which are often beautiful but very complex objects.

The image below shows a 4D structure made of 120 regular dodecahedra. This "shadow" of it has the form of one large dodecahedron filled in with 119 smaller dodecahedra. In 4D all the dodecahedra are regular, but in this 3D shadow, angles are necessarily distorted, so only the innermost and outermost dodecahedra appear regular.

Even more beautiful and intricate is the truncated 120-cell, a 4D object made of 120 truncated dodecahedra and 600 tetrahedra.

Below is two variants of a woven assemblage of Salamanders, in homage to M.C. Escher. The left image is a rapid prototype and right image is a laser-cut wooden sculpture.

Platonic solids with Escher's mosaics

With Escher's mosaics we can cover not only flat plane but also surfaces of platonic solids. Some Escher's tessellations can be divided into simple shapes such as triangle and square. Using these simple shapes we can cover facets of polyhedrons. Below, you can see several examples of covering of Platonic solids with Escher's mosaics.

These images was found at http://www.math-inf.uni-greifswald.de/mathematik+kunst/polyeder.html