An analysis of the Khodjah Akhmad pattern by M.S. Bulatov was published in THE ARTISTIC CULTURE OF CENTRAL ASIA AND AZERBAIJAN IN THE 9th–15th CENTURIES[br]Volume IV Architecture (Samarkand - Tashkent 2013) ISBN 978-9943-357-13-6 (IICAS)[br]The construction starts from an equilateral triangle and a square ending in a fascinating pattern of heptagons and 8-pointed stars. Follow the construction step by step in the applet below.

The construction starts from an equilateral triangle and a square ending in a fascinating pattern of heptagons and 8-pointed stars. Follow the construction step by step in the applet below.[br][list][*]Construct an equilateral triangle.[/*][*]Construct a square on one side of the triangle and draw its diagonals.[/*][*]Construct in the square a circle with a radius eqial to 1/4 of the side of the square.[/*][*]Construct a second circle with its center at a vertex of the triangle and tangent to the first circle.[/*][*]Divide 360° into 3 angles of 50° and 4 of 52.5° to construct an irregular heptagon.[/*][*]Construct additional triangles, squares, circles and heptagons by mirroring.[/*][*]Construct an octagon by elongating the sides of a heptagon.[/*][*]Now the square left below of the drawing of M.S. Bulatov is created.[/*][*]Further decoratio can be realised by elongating sides to create 7-pointed stars in the heptagons and to connect them by doubled lines.[/*][/list]

On the photo the part matching the construction in the applet is marked.[br]Notice that you have to look closely to mark that the heptagons and the 8-pointed stars aren't regular.[br]Notice also the difference between constructing a tiling using a system and realising a pattern on a building. On the right in the applet you see that elongating the sides of heptagons an octagon is created that marks the middle of the pattern of the mausoleum instead of keeping mirroring the pattern.[br]Equally the apex of the pattern isn't realised simply by repeating the mirroring of the construction in the applet but by locally deviating from it. This is typical for many patterns. One needs a skilled eye to see the very pragmatic adaptation of a so-called regular tiling by the decorators at first sight. Often it's just by drawing yourself you notice the combination of geometric knowledge and practicle skills.