Mathematics Professor Brigitte Servatius worked with us to develop the mathematical model on which the ARCX® dome is based. The model is highly precise, enabling us to design three dimensional ARCX® parts to an 8 decimal tolerance. The geometric building block of our dome design is the flat version of the smallest single spherical triangle that can be used to tile a sphere. It takes exactly 120 of these so-called Schwarz triangles, named after German mathematician Hermann Schwarz (1843-1921), to cover an entire sphere.