A Thirteenth-Century Dodecahedron in Central Anatolia: Geometric Patterns and Polyhedral Geometry

Sibel Yasemin Özgan; Mine Özkar

doi:10.1007/s00004-017-0341-0

A Thirteenth-Century Dodecahedron in Central Anatolia: Geometric Patterns and Polyhedral Geometry

Sibel Yasemin Özgan^*, Mine Özkar

^*Corresponding author for this work

Department of Architecture

Istanbul Technical University

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

The lace-like geometric patterns of medieval Seljuk art cover mostly planar surfaces, extending to the borders in a uniform manner. Some are applied on engaged columns, interiors of concave surfaces, and exteriors of half-spheres. There are also rare examples on faces of polyhedra. The construction of either the tessellation or a polyhedron is already demanding, and combining the two poses an additional mathematical challenge. One such case is that of the tomb of Gömeç Hatun in Konya, where a dodecahedral column capital was, as evidence suggests, covered with a mosaic tiling. A visual geometric investigation of the capital and its historical precedents sheds light on how the artisan’s knowledge of polyhedral and polygonal geometries may have been essential in the design and its materialization.

Original language	English
Pages (from-to)	455-471
Number of pages	17
Journal	Nexus Network Journal
Volume	19
Issue number	2
DOIs	https://doi.org/10.1007/s00004-017-0341-0
Publication status	Published - 1 Jul 2017

Bibliographical note

Publisher Copyright:
© 2017, Kim Williams Books, Turin.

Funding

This research is supported by The Scientific and Technological Research Council of Turkey (TÜBİTAK) under the project number 114K283, and under the 2211-Scholarship for PhD students program. All photographs and images are by authors except where noted. The assistance and kind interest of Prof. Dr. Ali Baş, Prof. Dr. Osman Eravşar and Dr. Şükrü Dursun in the research of historical photographs and references are gratefully acknowledged. We thank Konya Municipality, Department of Housing and Urban Development and Konya Cultural and Natural Heritage Preservation Board for providing restoration reports and drawings of the Gömeç Hatun Tomb. We also want to express our gratitude to Prof. Dr. Semra Ögel and Akbank for permission to reproduce the photo that appears here and to Şule Yiğit for hosting us in her studio for the making of the dodecahedron out of a clay cube.

Funders	Funder number
Konya Municipality
U.S. Department of Housing and Urban Development
Türkiye Bilimsel ve Teknolojik Araştirma Kurumu	114K283

Keywords

Design analyses
Design computation
Geometric patterns
Platonic solids (dodecahedron)
Polyhedron/polyhedra
Seljuk art
Tessellations/tilings

Access to Document

10.1007/s00004-017-0341-0

Cite this

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abstract = "The lace-like geometric patterns of medieval Seljuk art cover mostly planar surfaces, extending to the borders in a uniform manner. Some are applied on engaged columns, interiors of concave surfaces, and exteriors of half-spheres. There are also rare examples on faces of polyhedra. The construction of either the tessellation or a polyhedron is already demanding, and combining the two poses an additional mathematical challenge. One such case is that of the tomb of G{\"o}me{\c c} Hatun in Konya, where a dodecahedral column capital was, as evidence suggests, covered with a mosaic tiling. A visual geometric investigation of the capital and its historical precedents sheds light on how the artisan{\textquoteright}s knowledge of polyhedral and polygonal geometries may have been essential in the design and its materialization.",

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A Thirteenth-Century Dodecahedron in Central Anatolia: Geometric Patterns and Polyhedral Geometry

Abstract

Bibliographical note

Funding

Keywords

Access to Document

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