Art in Shadows of the Six-Dimensional Cube

László Vörös
Proceedings of Bridges 2011: Mathematics, Music, Art, Architecture, Culture (2011)
Pages 257–262 Regular Papers


The three-dimensional model of more-dimensional cubes can be constructed on a rotational axis and on the joining central point in symmetrical form, based on a regular polygon. An orthogonal projection of this kind of model of the six-dimensional cube shows an image, like the projection of the cube in the direction of its diagonal, perpendicularly to the plane of the image. The projection of any derived (6>j>2)-dimensional solid fits to the network of triangles joined by their sides in this method. The hull of the 6-cube’s 3-model may be the Archimedean truncated octahedron as well and the top view of the 3-model of a derivative 3-cube shows a special shadow casted by parallel beam of light. Based on all this, a reconstruction maintaining the topology of the forms made up of cubes, like hinted by the pictures for instance of V. Vasarely and T. F. Farkas, is possible. These hold latent unit mosaics of tessellations and in this manner may inspire to construct geometrical structures of further creations.