Abstract
This article analyzes two-dimensional images documented in the work of fourth/tenth century mathematician Abu al-Wafā' Būzjānī, which appear in his treatise, On Those Parts of Geometry Needed by Craftsmen. These images record three-dimensional tessellations of the sphere, geometric constructions, which may have served as a basis for architectural monuments and the interior design of domes in Islamic Iran. Such designs were very likely the result of collaborations among mathematicians and artists. As explained here, the construction of the icosahedron on a sphere, as presented in Būzjānī's treatise, is not mathematically correct. But the construction of the spherical dodecahedron is precise. Būzjānī's studies of the sphere as a three-dimensional form deserve further consideration as an important component in the development of mathematical thinking.
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