Reflecting the Regular Pentagon Role in Geometric Patterns of Islamic Architecture of Iran

One of the fundamental pillars of architecture and Islamic period decorations is using geometric patterns in the form of decorative surfaces named “Geometric decoration” (girih) In order to cover and spacing the Islamic monuments through different ages That without paying attention to geometry science, numbers and mathematics, drawing such girihs is not possible. One of these holy numbers, which is a symbol of flourishing and life, and also due to its concept and geometry, has played a significant role in the construction of girihs, is the number five. Hence, the present paper seeks to study the concept of geometry and its application, its relation to numbers and mathematics. Upon examining the Holy Number five, it identifies girih that can be drawn through a regular pentagon, and find the positioning and presence rate of other decorative motifs in these girihs. Finally, by studying the works in the Islamic monuments of Iran, it tried to find successful examples of those girihs. Therefore, in view of the final goal, this paper, by means of library studies and with the help of various sources and the study of linealhistorical documents, has descriptive-historical, analytical methods trying to reflect geometry and number five in Islamic geometric designs. The results of the research show that there are at least 10 types of girihs with a regular pentagonal motif. Due to its slow angles, it is not present in any of the "sharp girih". Contrary to the slow pentagonal angles, we see the presence of the “sharp Shamse 10” motif in two girih, along with the regular pentagon and in the "slow and sharp girih of the Giveh (Mooryaneh)", the sharp and slow Shamse motif are placed simultaneously in the same context, in spite of the discordance of the inner angles.

Specify the reflecting of the number five and the regular pentagonal motif in Islamic geometry patterns (girih)  Specify the positioning and placement of geometric decorative motifs in geometric patterns with regular pentagonal motif and determination of the frequency of other decorative motifs in the girihs with a regular pentagonal motif

Questions:

How is the manifestation and reflection of the number five, and especially the regular pentagon in Islamic geometry patterns? How is the placement and abundance of other decorative motifs in girihs that have regular pentagonal motif, and what are its examples in the geometric patterns of Islamic designs of Iran?