Found in Proposition 2 of Book VII of Euclid’s Eléments, the procedure now known as Euclid’s Algorithm computes the greatest common divisor of two numbers. Motivated by recent studies that have applied this algorithm to the analysis of rhythmic structures in music, it is extended here into the realm of architecture. A modeling algorithm is derived from the repeated subtraction method outlined in the original book. The output is then brought into a complex geometry format by using Mobius transformations to generate mappings onto the sphere. Dome-like forms are produced that await further architectonic development and evaluation.