APPROXIMATE INDEXING OF ICOSAHEDRAL POLYHEDRA WITH FIBONACCI NUMBERS

In general, indexing faces of icosahedral face-forms requires irration al numbers. However, for many practical purposes an approximate indexi ng based on triplets of integer numbers can be used. Two possible appr oaches called, respectively, ''Fibonacci Matrix Methods'' (FMM) and th e ''Linear Combination Method'' (LCM) are described. FMM relies on the use of ''auxiliary'' matrices F-n, F-n(2), F-n(3) and F-n(4) which ha ve Fibonacci numbers as their elements. These matrices allow good appr oximation of the results usually obtained using the standard five-fold rotation matrices which are typical of icosahedral symmetry. LCM is b ased on the use of a classical crystallographic rule i.e. the so-calle d ''Goldschmidt Complication Law'' which is just a particular case of linear combination of triplets of face indices, with integers as coeff icients. The occurrence of large integer indices is remarked.