tesselation with 5-fold symmetry

My head still throbbed lightly and the smell of the new scrubby grey floor tiles did not help to improve it. I concentrated on the unusual pattern of the otherwise ordinary floor covering. The tiles were light and dark grey and laid out in an unexpectedly complex arrangement. Areas can be filled completely and symmetrically with tiles of 3, 4 and 6 sides, but it was long believed that it was impossible to fill an area with 5-fold symmetry though Kepler played with the idea. I knew this because my mother loved the work of M.C. Escher who was intrigued by mathematic patterns and used them in his illustrations. It did perplex me that the library floor tiles were cut out of so called kite and dart shapes which actually allow a surface to be completely tiled in an asymmetrical, non-repeating manner in five-fold symmetry with just two shapes based on phi. As a result the tessellation of the dense felt tiles in the lobby made it impossible to arrange my thoughts according to the floor pattern – a technique I had used since childhood to soothe anxiety. Instead I began to draw shifting lines through the pentagrid in my mind, preferably coming up with glowing triangle shapes. The forms danced in front of my eyes. I felt faint.

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