Abstract

Symmetry: Culture and Science
Volume 31, Number 2, pages 177-198 (2020)
https://doi.org/10.26830/symmetry_2020_2_177

MATHEMATICAL CLASSIFICATION OF RUM SELJUK ORNAMENTS

Mehmet Erbudak¹

¹ Department of Physics, ETHZ, CH-8093 Zurich, Switzerland and Physics Department, Boğaziçi University, Istanbul, Turkey
E-mail: erbudak@phys.ethz.ch
ORCID: 0000-0002-6316-5115

Abstract: The group-theoretical classification of ornamental symmetries is a robust scientific method, which is applied here to the already published ornaments of Rum Seljuks. This mathematical method classifies the patterns into 17 wallpaper groups and allows us to compare the creative products of the craftsmen with those of other cultures. The analysis shows that the work of the Seljuks is concentrated in groups of mirror reflections in two perpendicular directions for the rotational symmetries 2, 4 and 6, as they are known for the Arab culture. Furthermore, there are patterns that are very similar to the Arab-Muslim work of art. We note that the work of the Rum Seljuks only bears some resemblance to the ornaments of the Great Seljuks, Byzantine and Armenian cultures.

Keywords: Ornaments, tessellation, group theory, wallpaper group, Rum Seljuks.
PACS 2010: 68.35.B-, 68.35.-p, 61.50.Ah
MSC 2010: 20H15, 14J80, 74E15

References:
Abas S.J. and Salman A.S. (1995) Symmetries of Islamic Geometrical Patterns, Singapore: World Scientific, xii+396 pp, 16 color plates. https://www.worldscientific.com/doi/pdf/10.1142/9789814335942_fmatter

Bourgoin J. (1876) Les Èlèments de L’Arabe, Paris: Librairie de Firmin-Didot, 246 pp.

Bourgoin J. (1973) Arabic Geometrical Pattern and Design, New York: Dover, 200 plates.

Critchlow K. (1976) Islamic Patterns, London: Thames & Hudson, 192 pp. https://archive.org/details/IslamicPatterns_201805/page/n1

Çok B. (2018) Tiled Mihrabs Decorations in the Period of Anatolian Seljuks on the Edge of Borders, K7AUIFD 5, 8, 201 − 208. https://dergipark.org.tr/en/download/article-file/495231

Emmer, M. (2013) Symmetry in Saint Marc’s Basilica, Symmetry: Culture and Science 24, 1 − 4, 215 − 226.

Erbudak M. (2019) Symmetry analysis of the floor ornaments of the San Marco cathedral in Venice, Heliyon 5, e01320 16 pp. https://doi.org/10.1016/j.heliyon.2019.e01320

Erbudak M. and Kyurkchyan A. (2019) Armenian, Byzantine and Islamic Ornaments – Influences Among Neighbours, Yerevan: Kyurkchyan 48 pp. https://doi.org/10.3929/ethz-b-000394011

Hammond C. (2015) The Basics of Crystallography and Diffraction, 4. ed., Oxford: Oxford Univ. Press, 542 pp. https://doi.org/10.1093/acprof:oso/9780198738671.001.0001

Hutt A. and Harrow L. (1977) Iran 1, London: Scorpion Publications, 191 pp.

Jones O. (1856) The Grammar of Ornament, London: Day and Son; (2016) Princeton: Princeton University Press, 496 pp.

Makovicky E. and M. (1977), Arabic geometrical patterns – a treasury for crystallographic teaching, Neues Jahrbuch für Mineralogie Monatshefte 2, 58 − 68.

Makovicky E. (2015) In the Footsteps of Maragha: Ornamental Panels in the Madrasas and Mosques of Esfahan, Konya, Agra, Sivas and Yazd, Symmetry: Culture and Science 26, 4, 421 − 441 gives an overview on the current understanding of medieval quasiperiodic creation in architecture.

Makovicky E. (2016) Symmetry, Berlin: De Gruyter, xix + 242 pp. https://doi.org/10.1107/S2053273317001747/

Mecit S. (2014) The Rum Seljuqs: Evolution of a Dynasty, London: Routledge, 318 pp.

Meinecke M. (1976) Fayencedekorationen seldschukischer Sakralbauten in Kleinasien, Tübingen, Vol. I: Verlag Ernst Wasmuth, xiv + 220 pp, 54 plates, 2 maps.

Müller E.A. (1944) Gruppentheoretische und strukturanalytische Untersuchung der Maurischen Ornamente aus der Alhambra in Granada, [Ph.D. Dissertation], Zurich: University of Zurich, 128 pp.

Müller E.A. (1946) El estudio ornamentos como applicatión de la teoría de los grupos de orden finito, Euclides (Madrid) 6, 42-52. Publishers home page https://www.worldcat.org/title/euclides/oclc/924470145?referer=di&ht=edition/

Schneider G. (1980) Geometrische Bauornamente der Seldschuken in Kleinasien, Wiesbaden: Dr. Ludwig Reichert, 204 pp.

Shechtman D., Blech I., Gratias D. and Cahn J.W. (1984) Metallic Phase with Long-Range Orientational Order and No Translational Symmetry, Physical Review Letters 53, 20, 1951 − 1954. https://doi.org/10.1103/PhysRevLett.53.1951

Tennant R. (2008) Medieval Islamic Architecture, Quasicrystals, and Penrose and Girith Tiles: Questions from the Classroom, Symmetry: Culture and Science 19, 2 − 3, 113 − 125.

Wichmann B. (2008) Symmetry in Islamic Geometric Art, Symmetry: Culture and Science 19, 2 − 3, 95 − 112.

Appendix:
Gerd Schneider has divided Seljuk ornaments into 50 groups, which in the original publication (Schneider, 1980) are referred to as Tafel. Here I use G for the group instead of Tafel. A figure in G is abbreviated as F. Below there are the same ornaments, but divided into plane-group symmetries. The locations of each ornament can be foundRef. (Schneider, 1980).

p1
G2F21.

c1m1
G19F214, G37F371.

p211
G3F23,31, G10F81,83,85,86,87,89,90, G11F94, G18F204.

p2mm
G18F205,207,212, G20F224, G36F74,360,362,363,366,367,369,370, G37F372,375, 380,382, G38F384,386,387, G39F388,390, G43F416,417,418, G44F420,421,422,444, G45F424, G48F431,432,433.

p2mg
G3F30, G6F41, G36F361.

p2gg
G3F26,29.

c2mm
G3F22,27,28, G16F179, G17F201,203, G18F209, G19F216,219, G26F277,281,282, 283, G27F297, G30F322,327, G31F330, G36F364,365,368, G37F373,374,376, 377,378,379, G38F383,385, G39F389,391,392.

p3
G7F45,53, G18F211.

p31m
G7F46,47,48,49,50,51,52.

p4
G2F14,15,16,17,18,19,20, G3F24, G5F36, G6F40, G9F69,70,71,79, G10F80,82,84, G11F91,93,97,98, G12F103,104,105,106, G15F169,170, G16F182, G27F292.

p4mm
G15F159,161, G16F171,172,173,174,175,176,177,183,184,185,186,187,188,189, G18F210, G19F217,220,221, G20F222,223, G26F276,278,279,280,284,G27F287,288,289,290,291,292,293,294,295,296,298,299,G28F300,301,302,303,304,305,306,307,308,309,G29F310,311,312,313,314,315,316,317,318,319,G30F320,321,323,324,325,326,G31F328,329,331,332,333,334,335,336,337,G32F338,339,340,341,342,343,344,345,346,347, G33F348,349,350,351,352, G41F404,405,406,408, G42F409,410, G45F423, G46F425,426,427,G47F428,429,430.

p4gm
G3F25, G6F39, G9F76,77,78, G10F88,G13F158,160, G16F178,180,181, G26F285,286.

p6
G6F37,38,42,43,44, G7F54,55,56, G8F57,58,59,60,61,62,63,64,65,66,67,68, G11F95,96, G12F99,100,101,102, G13F107, G15F166,167,168, G17F198.

p6mm
G15F162,163,164,165, G17F190,191,192,193,194,195,196,198,199,200,202, G18F206,208,213, G19F215,218, G20F225,226,228, G21F229,230,231,232,233,234,235,236,237,238, G22F239,240,241,242,243,244,245,246,247,248,249, G23F250,251,252,253,254,255,256,257,258,259,442, G24F260,261,262,263,264,265,266,443, G25F267,268,269,270,271,272,273,274,275, G34F353,354,355, G35F356,358,359, G40F394,395,396,397,398,399,400,401,402,403, G41F407, G42F411,412,413,414,415,441, G49F434,435.