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.

Anamorphic art

The word anamorphic is from the Greek "ana" (again) and "morphe" (form). It refers to images that are so heavily distorted that they are hard to recognize without the use of a mirror, sometimes referred to as an anamorphoscope. When viewed in the anamorphoscope, the image is "formed again", so that it becomes recognizable.

Anamorphic art as known from middle ages. European painters of the early Renaissance were fascinated by linear anamorphic images, in which stretched pictures are formed again when viewed on a slant. A famous example is Hans Holbein's "The Ambassadors" (1533), which contains a stretched-out skull.

Nowadays anamoprhic art is rised again because of works of such famous artists as István Orosz, Kelly M. Houle, Julian Beever and Felice Varini.

Hungarian artist István Orosz is well known for his artworks with impossible figures and constructions. He also tries to renew anamorphosis art. Frequently he uses etching tecnique for his artworks. Below you can see two views of his artwork "The Well" (1998). You can see the original image to the left, and a part of the same image with cylindrical mirror in the center of the well. We see face of M.C. Escher in the mirror.

Kelly M. Houle also creates anamorphic images for cylindic mirror. She working on projects including illustrating a children’s book manuscript, writing and illustrating a trilogy of fictional correspondence with an anamorphic theme. Below you can see anamorphic portrait of Leonardo da Vinci.

Julian Beever creates his artworks by chalk on roads and streets. His paintings can be viewed as real image from one point of view only.

Felice Varini paints (lines, concentric circles, triangles) on things (tunnels, castles, groovy interiors). A seemingly random smattering of elements that, viewed from a specific point in space, coalesce into a tangible planar element.

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