One of the greatest challenges of the architecture during the
old days was figuring out how to place a circular dome over a square building. Early
attempts with slanted square slabs to make a octagonal shape was irregular and failed. In
the fifth century the Byzantine and Sassanians started to use the squinch, an arched vault
or half dome, which were placed across the corner angles. The Muslims started to use this
method with great success. Instead of plane squinches, they started to use decorations.
1. Leacroft, Helen and Richard, The Buildings of Early Islam, London, Addison-Wesley Publishing Company, 1976