Gummelt draws Petra Gummelt’s quasiperiodic tiling of the plane with overlapping decagons.

Decagonal tile

This tiling is related to the rhombic Penrose tiling, with a decagon associated with each “fat” rhomb, and the side-matching rules replaced by the requirement that wherever two decagons overlap, the coloured darts they contain are superimposed. Each decagon contains four darts, two of them pointing clockwise and two pointing counter-clockwise, with one pair overlapping.

In the applet, the darts are given two different colours, based on their orientation; the result is a tiling by two different kinds of decagons, in the sense that they have different colouring schemes for the darts, but exactly the same arrangement results if all the darts are coloured identically. The associated “fat” Penrose rhomb is superimposed in grey.

Reference: New Scientist, 27 February 1999.

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