Finding Unique Triangulations of a Polygon using Frieze Patterns
A Wallpaper group is a mathematical pattern that repeats or has translations in two directions in the plane. Frieze
patterns, similarly, are mathematical patterns that repeat or have translations in one direction. These kinds of patterns often
occur in art and architecture such as in the immortals’ archers in Persepolis, wall decorations in Alhambra, intriguing
drawings of Maurits Cornelis Escher and many more. Frieze patterns are generally determined using triangulated polygons.
This paper reverses the approach and establishes solution to find triangulated polygons belonging to a particular frieze
pattern. Furthermore, this paper contrives a new way to calculate the number of unique triangulations of a polygon using
Keywords - Frieze Pattern, Triangulated Polygons