A tiling of a surface is a decomposition of the surface into pieces, i.e. tiles, which cover it without gaps or overlaps. In this paper some special polygonal tiling of sphere, nellipsoid, cylinder, and torus as the most abundant shapes of fullerenes are investigated.

Relative peace of country in the Safavid era under the centralized First Shah Abbas reign, led to construction works in big cities. According to recognition of Shia religion in this era, and as a result, existence of a need for educational facilities in order to promotion of this religion, school-building tradition was popularized in this era more than other eras. In this regard, many schools were established by scholars, elders and rulers in the cities. Gradually, impressive attention was paid to architectural decoration in both inner and outer spaces of schools. tiling, brick work, Ma’ qeli and Karbandi decorations, and etc. are among decorations existed in Iranian schools. Usage extent of the mentioned decorations has been different in different eras. Khan School in Shiraz is one of the most important schools constructed by the rulers of Shiraz, Allah-verdi khan and his son Emam-Qoli Khan in this era. This school possesses a unique luster with four-porch pattern, chambers in two floors, a long gate, and various decorations such as Mogharnas, mosaic and seven-colored tiling with distinguished motifs and colors. This building is significant enough that has been mentioned in almost all of historical references and tourists’ travelogues in different eras. This school is significant from the architecture and architectural decoration, especially tiling points of view; and according to professor Pirnia, it is one of the most perfect schools in Iran from the plan and architectural decorations point of view. One of the obvious characteristics in the tiling decoration of this building, is the existence of different motifs in various styles. In addition, tiling in this building has a quite different color comparing with tiling in Safavid era buildings. The other point is the impressive similarity of its converge ceiling tiling with dome ceiling tiling of Sheikh-Lotf-o-Allah mosque in Isfahan. According to the construction date of the building and variety in its motifs and colors used in tiling decoration, the following question will arise; “ are these decorations related to Safavid era? Or they have joined the building during subsequent eras? Likewise, with which buildings do the motifs characteristics existed in tiling decoration of this building match? The main purpose of this study is, introduction, classification and checking the motifs existed in tiling decoration of Khan School of Shiraz. The approach of study is descriptive, comparative and data collection has been performed through field study and library method. According to occurrence of several civil wars, earthquakes, gradual erosion of the building and nonconformity of correct repair principles, architectural decorations and even the building plan have been basically changed. Obtained results suggest that most content of architectural decorations in Khan School of Shiraz includes Qajar and contemporary seven-colored tiles with herbal, bestial, geometric motifs and Quranic inscriptions in hot colors which have gradually replaced the decorations of Safavid era. Remained decorations from Safavid era have been affected by important buildings such as: Sheikh-Lotf-o-Allah mosque and Imam mosque in Isfahan due to the construction concurrency with these significant buildings.

Due to avoiding utilization of human figures and abstaining from idolatry, decorations have specific geometry in Islamic art and architecture. One of the striking characteristics of the knots (girih) that has caused to dynamicity throughout its thousand-year history is its regeneration and diversification of the diverse geometric properties. Girih tiling decoration is part of geometric arts in the traditional buildings of the historic town of Masouleh dates back to eight hundred years. Traditional and local architects of this historical town have adopted special and intellectual plans for creating visual attractions in expression and creation of girih tiling in the walls of the monuments. One of these valuable solutions is diverse geometric decorations patterns. Since the main facades of the houses in this town are directly located in the sunrise direction and it is accepted landscape for the citizens of this historical town, so the artists have shown their art and style in this part of the monument and built beautiful and harmonic diverse wooden windows and variety of these patterns are seen in all five neighborhoods in this town. Girih tiling consists of straight and broken lines on a regular basis that could be reasonably expanded in the surface. In the present study, it has been tried to classify the decorations in girih tiling in the neighborhood of Masouleh and also investigate girih tiling including scrolls and edges, and also the role of decoration in this element. The methodology of the research is based on field study and direct observation of the monuments and decorations and taking image and converting into Auto CAD files with dimensional analysis. Also, for description of girih tiling, descriptive and library studies have been conducted. Questions that the research seeks to answer in this paper are: Can it 8 D be offered a defined pattern for opening girih tilingby analyzing of the decorations in neighborhood of Khanehbar in Masouleh? And also is the largest usage of the patterns seen in scrolls (middle or central plan)? Does scroll use most patterns in its margins? The girih tiling patterns of “gavarehbari” with “boteh jegeh” designs (paisley), eight squares ornamental layout, rectangular, “hasht-chahr longeh tokhmedar”, and gavarehbari with the scales patterns are more common patterns. Fourteen patterns were seen in studying the girih tiling patterns employed in the combined windows that “alat jafari chokhati” and then rectangular tiling and seven and eight sides tiling patterns were common. The patterns used in the friezes are mostly eight squares layouts. The most common patterns in the margins are four- side tiling in all parts. Diverse patterns of girih tiling, besides with diverse combinations resulted from placing together and offering shapes in the friezes and marginal patterns have offered rich visual ornamentation in the historical city of Masouleh. Such studies aid reproduction of these patterns in the contemporary fine arts while preservation and documentation of the fine and visual patterns in the Iranian girih tiling.

This paper describes an algorithm for tiling with polyminoes that consider rotation and/or reflection of figures in the steps of 90o. First, we review the previous parallel algorithms for tiling problems. Next, we propose a hybrid approach that is based on genetic algorithms (GA) and artificial neural networks (ANN). In this approach, the production of new members in GA and their evaluation are performed by a Hopfield neural network. Finally we compare our method with the previous works, and show that our method can produce global minima for many problems. The algorithm can be used for solving a variety of 2D-packing problems.

Qajar period can be seen as innovations and new developments in art and architecture. Among these developments, the growing relationship and exchanges with the West, Seeking new knowledge and new science to Iran, Special effects seen on the Art and Architecture and especially buildings decoration are in the Qajar period.Among the most important developments and New knowledge can be cited invention and log in photography, Log in and application of correspondence postal stamps and New European postcards.In this article, research methods is used description- Analysis and Studies Library in Architecture of The Masjid-Madreseh and also Field Studies To participate in the building and Direct observation. And the impact of these developments Review and assessment has been on the decorations Mashid-Madreseh of Qajar.Based on the reviews and studies, much of the decorating and tiling designs Mashid-Madrseh of Qajar is modeled Photos, stamps and postcards of that period.And images of monuments, Landscapes and architecture, Birds, grapes, crown, winged angels and humans, European men' s clothing, The flower vases and bowls and plates With various flowers, especially roses and lily In designs and decorative tiling And sculpted monuments seen.

Magnificent and beauty contributed to the architecture, especially during the Islamic era, is due to the decoration of the buildings. Chahar Bagh masjed-madreseh (mosque-school) in Isfahan is one of masterpieces of Safavid period and also masjed Seyyed is Isfahan is one of the buildings built in the early Qajar period, especially in terms of decoration and tiling patterns.Review, study and comparison of tiling patterns of the two buildings Can be recognized the cultural identity of these two buildings. The present research is based on the relative lack of scientific study of the historical architecture of the schools buildings in our country especially in the field of decorating and using analysis-description method and library studies in the field of architectural decorations of the two buildings and the field studies, tries to assist and compares the tiling patterns of the two distinctive buildings from Qajar and Safavid eras.Research findings show that the geometric and plant motifs on the tiles, decorating most of Chahar Bagh School, is abstract which benefits from a simple and fluent solidity, of which the decorative handwriting is dominantly Kufic and thulth handwritings. In masjed-madreseh Seyed, the decorative images such as fruits, grapes, flowers, vases, bowls, landscape and plates have been used in a high multiplicity and also applied, under the impact of decorative arts, in the West, as some realistic, abstract and non-duplication designs. Nastaliq hadwritiing is the most dominant in the inscriptions.

The history of the shrine of Imam Reza (AS), the most important attraction of religious tourism in Iran, dates back to more than ten centuries ago, which was decorated with various decorations during the Islamic states; and each section represents the art of architecture of the special era of Islamic art history. Characters and elders have been renovating and developing this scared place in every age. Allahverdi Khan, a brave warrior and military commander of Safavid era, paid special attention to the architecture of this era, and he has done a great deal to raise the culture and civilization of Iran; this can be emphasized by the culture and civilization of Iran; by looking at his remains in Esfahan (Si-o-se-pol), Shiraz (School of the Khan) And Mashhad (Dome of Allahverdi Khan). This magnificent building is one of the most beautiful buildings in the holy shrine that Arthur Pope, in the book of Iranian architecture, considers the most complete part of the shrine of Imam Reza (AS). The mosaic tiles of this porch are decorated with inscriptions, animal motifs, plant, and geometric designs. Many of these motifs are conceptualized, which have a particular place in the culture and literature of this boundary. In this regard, the present study was conducted using descriptive and content analysis based on field observations and library data. Among the 487 roles in 9 species of animals, each of which is a world with full of mysteries, the highest number motifs include the motif of the bird (chicken) and then there are, respectively, pheasant, parrot, peacock, duck, dragon, simurgh, deer and Chicken Bismillah. Research purposes: 1. to introduce the symbolic of the animal motifs in porch of Allahverdi Khan. 2. The study of symbolic concepts of animal motifs in the mentioned porch. Research Questions: 1. what are the types of animal motifs in porch of Allahverdi Khan? 2. What are the symbolic implications of this motif?

Positive and negative spaces in the timing of the mosques not only create equilibrium and balance, but also contain spiritual meanings. But, during different eras, due to influences of external effects, manifested this noble concept, has been declining.In this paper, the positive and negative spaces based on mystical and philosophical concepts, in the tiling frames in the mosque of Imam Khomeini (RA) in Isfahan, the Safavid period and the mosques and school of martyr Motahhari as an evidence of Qajar architecture, has been studied. In addition to investigation and analysis of the positive and negative spaces of the tiling of the ‘’Shahid Morahhari’’ school, decorations of this school also has been compared with ‘’Imam Khomeini’’ School as a well-known structure remained from Safavid dynasty that by this way, determine the rate of Changes in the transcendental concepts of visual symbols which were affected by Western art. So that by changes in the fundamental symbols of this type of tile work of art, also dramatically their concepts change and become transformed. Using a valid index to convey the deep concepts in the foundations of decorating items to present era is so important. According to the investigations, using fundamental items like positive and negative spaces in this school show how consistent they are with values and deep and conceptual criteria of the far past and how much they have changed.Research method in this paper is descriptive analysis and utilizes by comparison system in the idiom analysis.

Discussing Islamic architecture without considering decoration is not perfect; because decoration is an essential part of Islamic architecture. A major part of Islamic architecture is devoted to decoration and it plays a spacious and valuable role to achieve the goals.These decorations could include the smallest parts of architectural material in the simplest possible way to the most leading parts of architecture like colottes, harems, with the most complex form of various kinds of materials in geometric and abstract ways.Decoration has used in Ali Qapu building are involve fresco, Keshtebory, stalactite, tongbory, tiling, layechini.

The studies conducted so far on the Herat school’ s painting were more related to the aesthetic aspects and paid rarely attention to them in realistic perspective. One of the realistic features in paintings of the school was the reflection of Islamic architecture and decorative elements attached to it. Little attention to investigate the decorative elements in paintings stems from this presumption that Iran’ s painting mostly shows the world of Ideas and is far from the visible reality. In this paper, it is attempted to investigate the realism of tiling decorationsof theBehzad’ s paintings by removing the existing presumption. The present study seeks to answer the question that what extent is the status of using the motifs and tiling decorationsin Behzad’ s paintings and their adapting to decorative motifs of its contemporary architectural monuments’ tiling? The research method is descriptive and analytical based on library data. For this purpose, 8 Behzad’ s paintings were selected and their tiling decorations have been analyzed. Then, the comparative comparison was performed among each type of the decorations identified with the same decorations in established monuments of the Timurid era. Results indicate that most tiling decorations of paintings are affected by the real monuments of the Timurid era in terms of form, structure and color, and the common types of decoration used in paintings are under glazed tiles, geometric faience mosaic, geometric monochrome and then brick’ s Girihchini and painted tile through matching the decorative motifs and the accuracy of structure, while some other common types of the Timurid era’ s tiling such as geometrical under glazed, mosaic floral, geometric Moaqely and masonry ones have not been used in Behzad’ s paintings.