Analysis of Repetition Pattern and Geometric Characteristics of Regular Bases in Karbandi

The Karbandi is one of the original elements of Iranian architecture that has been an outcome of Iranian architects' dominance on geometry and mathematics. Designing Karbandies, choosing the base is a crucial key. It has always been a question "How to easily found related Karbandies for a Specific base?" and "By what pattern are the regular bases in Karbandies repeated?'. The present study is done to answer these questions. To achieve this goal, first, all the drawable Karbandies were drawn and then the bases in them were examined and explored. Bases in Karbandies were divided into two general coincidental and non-coincidental categories. Then the number of Karbandies with squares, rectangles, equilateral triangles, and regular polygons and corresponding repetition pattern for each plan was determined. It was shown that for each regular polygon the general pattern of repetition is an=kn*n k, nϵN. Also, the relationship between chord length in planar geometry of Karbandi, the height of Karbandi, and area of Shamse was examined and it was stated that the more we move in the types of one specific number of Karbandi, the length of the chord, the height of Karbandi and number of internal divisions in its geometry increases, but the area of the Shamse decreases. Besides, by examining a special type with the ability to generalize to all number of Karbandies, it was concluded that the length of the chords and consequently the height of the Karbandi is decreasing, but the area of the Shamse is increasing.