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 Gome double dagger 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.