The Third Dimension of the Magdouh Mosaic in Antioch

Abstract

This study investigates the complex geometry of the pattern of circles in the Magdouh Mosaic, which dates to between the fifth and sixth centuries, found in Antioch-on-the-Orontes (modern Antakya, Turkey). The mosaic has a complex pattern that is composed of tangent, overlapping and intersecting circles suggesting that it was worthwhile analyzing in 3D. Through such an analysis, it was observed that the extension of the pattern of circles into a third dimension looks like spheres packed together that intersect in three directions at right angles. This can also be demonstrated by packing octahemioctahedra, which are a cluster of eight regular packed tetrahedra contained within the spheres. In addition, the packing of octahemioctahedra in this way also suggests the packing of stella octangula contained within hemispheres that intersect each other. Furthermore, tracing the line segments that are emphasized in each circle in the Magdouh Mosaic in such a 3D structure turns them into space-filling rhombohedra that can be dissected into two tetrahedra and an octahedron. Thus, the result of this study shows that the Magdouh Mosaic in Antioch is the top view of a square-based pyramidal cluster of intersecting hemispheres that hold space-filling rhombohedra inside them.