When space is at a premium in any given city, high housing density is a top priority. That means more plentiful and affordable housing for everyone, but this usually comes at the cost of grassy yards for residents to enjoy. Gaze out onto the city of Takamatsu, Japan from an overlook point along the mountainside, and you?ll see almost no private outdoor space among the closely-set houses and apartment buildings, let alone rolling green hills covered in lawn chairs and native plants.

That is, until “Greendo” (Miyawaki Gurindo) came along. Architect Keita Nagata of Keita Nagata Architectural Element came up with a novel design for urban housing that produces spacious apartments topped with an undulating ribbon of rooftop gardens, all on a challenging sloped plot. Built into the foot of Mineyama mountain in the Kagawa prefecture, the complex takes advantage of the natural insulation and geothermal temperature control of the soil. The complex is fully passive, ?living and breathing? with the land. Each of the five housing units is buried into the slope to maintain a stable indoor temperature of around 59 degrees Fahrenheit, with ventilation pipes bringing in fresh air. Buried tubes bring up cool air from the mountain in the summer and warm air in the winter.

Steel-reinforced concrete makes up the outer walls for earthquake stabilization, and layers of anti-humidity insulation prevent moisture problems. An additional insulating layer of air between in the inner wall...