# Vladimir Bulatov

My artistic passions are purely mathematical images and sculptures, which express a certain vision of forms and shapes, my interpretations of distance, transformations and space. In my opinion, mathematics is a way of thinking, a way of life. My images and sculptures are like photographs of interesting mathematical ideas, which I try to dicover and to bring to the real world. I have always been intrigued by the possibility of showing the intrinsic richness of the mathematical world, whose charm and harmony can really be appreciated by everyone.

This is horosphere cross section of hyperbolic space tiling
generated by reflections in the

faces of Coxeter polyhedron combinatorially equivalent to a cube
with one truncated vertex. To color the tiling we select an index
7 subgroup of the total symmetry group of the tiling and color in
7 different colors interiors of the tiles, which belong to
different cosets of the subgroup.

This is a tiling at the infinity of hyperbolic space. The tiling
is

generated by reflections in 4 planes. The planes arrangement

is obtained from faces of hyperbolic tetrahedron by truncating one
vertex and

one of opposite edges and moving points of truncation to
infinity.

The interplay of reflections forms circular area with infinitely
many circular holes filled with two dimensional hyperbolic
triangle tilings (2 3 24).

To color the tiling we use different subgroups of the total symmetry group.