Flat Tessellations in Search of a Dome Shape

Based on the design solutions of the Orthodox Church and while maintaining the conventions of polyhedral surfaces, the author describes and analyzes new 3D geometric solids (structures) modeled on tessellations. The pretext for undertaking the research was the need to find a polyhedron shape that could replace the curvilinear shape of a burning candle flame that had been used for centuries in Orthodox church architecture. The innovative idea of designing polyhedral domes of Orthodox churches led the designer to interesting structures that are not derived from either regular or semiregular polyhedra. These objects, according to the author, constitute a kind of bridge between flat tessellations and three-dimensional semiregular or regular polyhedra. Their analysis unexpectedly leads to the source, which is precisely flat, semiregular tessellations.

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