yuko nagayama cuts folding courtyard into this 'diagonal house'

diagonal house: an architectural Exploration of Geometry

The Diagonal House by Japanese architecture studio Yuko Nagayama & Associates stands as an architectural solution tailored to a family of five in a residential area of Tokyo. Situated on sloped land nearly three meters above the road, this house blends privacy with an intimate connection to its surroundings. The client’s main request was for an enclosed garden space that would offer seclusion from the neighboring homes.

The design of Diagonal House was inspired by a simple geometric concept. The team began by inscribing a ten-meter square to align with the near-square shape of the plot. From this square, two diagonal lines were drawn to create four right-angled isosceles triangles. One of these triangles was designated as a garden, bringing a secluded courtyard for the family. The remaining space was developed with a focus on creating a series of overlapping and interconnected areas, each defined by the geometry of triangles.

images © Nobutada Omote

isosceles atriums by yuko nagayama

The design strategy by Yuko Nagayama & Associates extends vertically with the second floor using a rectangular slab that divides the Diagonal House in half. This division results in two smaller isosceles triangular atriums, which are symmetrically positioned to create a dynamic play of light and space between the floors. These atriums provide both visual and physical connections throughout the house, enriching the living experience by bringing natural light deep into the interior spaces.

The use of geometric shapes in Diagonal House continues the studio‘s exploration of form and space, as previously seen in the Japan Pavilion at the Dubai Expo. There, isosceles triangles were employed to fit within a trapezoidal site, demonstrating a fascination with the spatial possibilities offered by angles of 45 and 90 degrees. For Diagonal House, the simplicity of these shapes guided the design process, similar to folding a square piece of origami, exploring how rich and varied experiences could emerge from a straightforward structural approach.

Diagonal House is designed for a family of five, focusing on privacy and connection with nature

angled, sunlit interiors

From the outside, Diagonal House presents itself as a concrete box perched atop a hill. Upon entering, visitors are at once met with the corner of a triangular garden at the end of a short corridor, introducing the theme of geometry and nature’s interplay that continues throughout the house. The interior layout of Diagonal House revolves around the triangular garden. The main living space, featuring a triangular atrium, lies to one side, while a similar atrium marks the dining area on the opposite side. These areas are designed to embrace the garden, providing a constant visual connection to the outdoors. The atriums not only serve as light wells but also act as focal points that guide movement and interaction within the house.

The second floor houses compact private rooms primarily used for sleeping. These rooms are arranged along a corridor that faces the atriums and garden, ensuring a connection to the home’s central features. The corridor doubles as a workspace with a long desk that extends along its length, offering a communal area where each family member can study or work. Bookshelves filled with children’s textbooks and family favorites line the corridor, making knowledge and leisure readily accessible and reinforcing a sense of shared family life.

the house’s layout is based on a ten-meter square divided into right-angled isosceles triangles