Twins: Houses in Five Parts is an architectural project in upstate New York, for two brothers and their families who don't mind spending their vacations together, as long as they can retire to separate (neighboring) quarters. The overall structure is also some kind of mathematical meta-homage to the brothers' relationship as parts of a whole (twins are weird, as usual), but I'll let O'Brien explain that below.
"This design proposal for two vacation homes for two brothers and their families on one plot of land in upstate New York represents an examination of a curious part to whole relationship. The mathematical principle of "dissection" states that any two regular polygons with equal areas can be divided into sets of similar shapes; "minimal dissection" is the pursuit of the fewest number of subdivisions in each polygon. This scheme appropriates this principle as a solution to (1) general similarities in the programmatic requirements, and (2) distinctions in the desired relationships to the site, voiced by the two brothers for each of their homes.
A regular six-sided polygon and a regular four-sided polygon contain the same five shapes—each are made up of the same four trapezoids and one triangle. The adjacencies between the five shapes are different within each of the regular polygons, as are their orientations relative to the outer perimeters of the polygons. Translated into spatial divisions in an architectural plan, these fixed arrangements prompt sectional-flexibility. Conceptually, in section the floor planes and the roof planes are configured in order to accommodate strategic micro-topographic continuities and discontinuities across the collective surfaces.
Twins: Houses in Five Parts by William O'Brien Jr