Perfect colourings of cyclotomic integers
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- Bugarin, E.P., de las Peñas, M.L.A.N. & Frettlöh, D. Geom Dedicata (2013) 162: 271. doi:10.1007/s10711-012-9726-0
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Perfect colourings of the rings of cyclotomic integers of class number one are studied. It is shown that all colourings induced by ideals (q) are chirally perfect, and vice versa. A necessary and sufficient condition for a colouring to be perfect is obtained, depending on the factorisation of q. This result yields the colour symmetry group H in general. Furthermore, the colour preserving group K is determined in all but finitely many cases. An application to colourings of quasicrystals is given.