Kinetic sculptures by Haruki Nakamura

Look at the photo a heart sculpture above, which is consists of closely interconnected gears. Although it seems that gears cannot move it is not. All of them can rotate around their respective centers, which your can see on a video below. Moving of gears are shown approximately on 50th second of the video but it's 

This kind of sculptures are called kinetic because all parts of them can move. It was created by Japanese engineer Haruki Nakamura and represented in 2005 with title Gear's Heart. Unfortunately, there's no any more information about him in the Internet except several images of his sculptures and few videos.

Also he created similar sculpture of cube, which you can see below.

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.

Hilbert curve

Hilbert curve is a continuous fractal space filling curve, which was first described by German mathematician David Hilbert in 1891. Below you can see 5 first steps of the plane Hilbert curve.

But the Hilbert curve looks more interesting if it represent in three dimensions. Carlo H. Séquin, a professor of Berkley, created a small 5" metal sculpture of Hilbert curve, which he called "Hilbert 512". You can see it below.

It was also be modeled by Torolf Sauermann in the program Maxwell renderer. Below, you can see the second step of the three-dimensional Hilbert curve and two versions of cubic Hilbert curve.

Staircase knot

This strange composition of staircase reminds Möbius strip, but unlike Möbius strip this figure has two sides. So someone, who will try to rise this stairs, will continue rising infinitely returning to the starting point.

The sculpture also reminds one of the famous Escher's images "Knots". One of the them you can see below. This knot is also not a Möbius strip, because it has four sides.

Black cube by Gregor Schneider

German sculptor Gregor Schneider was fascinated by artwork "Black square", which was created by famous russian artist Kasismir Malevich, and he decided to create an analogue of it as sculpture.

Firstly, he tried to represent 15-metres high black cube in 2005 and was erected in Venice at International Art Exhibition - La Biennalle de Venezia. It was named "Cube Venice 2005". But his application was rejected by Venice authority for politic reasons because they were afraid to offend muslims who could consider it as recostruction of the holiest place of Islam - Kaaba, which is at the center of the Great Mosque in Mecca.

In 2006 Gregor Schneider with his cube was invited to exhibition in Berlin Museum of Modern Art. He renaimed it to "Cube Berlin 2006". But his participation in the exhibition was rejected again at the last moment by the general director of Berlin public museums.

Nadeem Elyas, the president of the central Muslim coulcil in Germany, advocated the cube, and finally, 14-metres high sculpture of black cube have found its place before Museum of Modern Art in Hamburg.

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.

Structures by Rinus Roelofs

Holland artist and mathematician Rinus Roelofs constructs charming mathematical structures. He constructs his structures in computer but some of them became sculptures in various Holland towns.

The sculpture above was erected in Borne (Holland) in 2005. It consists of 26 tetrahedrons or 104 triangles. Triangles are just slid together. Construction is stable and need no further fixing.

Bet he created a lot more computer models of three-dimensional structures. One of them (below) shows Hamiltonean path of polyhedron. Hamiltonean path is a sequence of edges that visits all vertexes of a polyhedron exactly once.

Besides three-dimensional structure Rinus Roelofs created a set of two-dimensional tessellation structures for Escher Centennial Congress in Rome in 1998. They represents regular structures that constitute infinite impossible figures. He insists not to call them tessellations but joins.

Sculpture of Sierpiski triangle

This giant sculpture represents three-dimensional version of fractal named Sierpinski triangle. This large tetrahedron that consists of 1024 smaller tetrahedrons was created by students of Alan A. Lewis School. Order of fractal is 6.

Metal sculpture by Kenneth Snelson

Kenneth Snelson creates his airy sculptures from metal. His structures are not hard joined but exist due to tension of individual elements. A term tensegrity was suggested structures of this type as combination of two words tension and integrity. Kenneth Snelson describes tensegrity as "a closed structural system composed of a set of three or more elongate compression struts within a network of tension tendons, the combined parts mutually supportive in such a way that the struts do not touch one another, but press outwardly against nodal points in the tension network to form a firm, triangulated, prestressed, tension and compression unit."

Cutting a wire in a tensegrity structure causes a major deformation or collapse.

Using principle of tensegrity he created many towers and other sculptures from aluminium and steel. You can see two photos of 60 feet high sculpture "Needle Tower" which was created in 1968. To the right is the front view of the tower and below is view from the basis of the tower.

Kenneth Snelson was born in Pendleton (Oregon, USA) in 1927. Educated in University of Oregon and Chicago Institute of Design. He had took part in many personal and grouped shows. His sculptures are in many collections and museums.

Bathsheba Grossman - A Twist In Time

Bathsheba Grossman (2002)

A Twist In Time

This snow sculpture was entered in the Breckenridge International Snow Sculpture Championship, 2002. Its genus is that of a Klein bottle with one handle and two holes, so it has one side and two edges.

Impossible triangle in Perth

A 13,5 metres aluminium sculpture of impossible triangle was erected in Perth (Australia) in 1999. It's the biggest sculpture of impossible figure in the world. Many people who live near the sculpture do not suspect that it represents impossible figure because it looks like impossible object from single point of view only.

You can see it at Google maps in the center of the round about. You can clearly see the arms of the triangle going off in different directions.

Triple Klein bottle

This is a glass sculpture which consists of three Klein bottles inserted one to each other.