The pentagrid as a device for the study of Penrose tilings

When studying Penrose tilings, one can dene the pentagrid which can be asso- ciated with a pattern arising from two fundemental building units: rhombuses with coloured and oriented edges.
It turns out that every pentagrid generates such a rhombus pattern. In general, there is a duality between pentagrids and these patterns.

Work with the pentagrid can be reduced to several parameters from which prop- erties of Penrose tilings in the form of rhombus patterns can be derived.

This work is concerned with the parameters of the pentagrid and with the infor- mation that can be deduced.