Hexagonal tiles made by the Portland Cement Company continue the pattern in the bathroom, where the architect designed low drawers and cabinets that are easy for Luna to reach.

The house's triangular shape effectively blocks sight of a large wall that stands nearby. "The form of the plan really follows out of making the best for the garden and the views," Koolhaas says.

“We tried to envision just two floors, but once summer arrived we decided that we were going to tear the roof off and put on that triangle with windows.”

“My favorite spot is the kitchen,” says Kaja Taft of the prefab home she shares with her family in Portland. “I can stand in it and cook and converse with everyone.” The space overlooks the back yard. The white-oak cabinetry is by HOMB and the countertops are Caesarstone. A hood by Faber is above a Dacor range.

Alex Monroe Studio (DSDHA: London, United Kingdom) This three-story timber-framed addition to a triangular building in London houses a custom jewelry studio. As a reflection of the craft occurring inside, the wood will patina over time, revealing wear and age.

Foundation Table with Triangular Base by Fort Standard, $2,600.

The triangle is the home’s leitmotiv, appearing in the cantilevered bedroom module and the steps approaching the entrance.

At 5 inches tall and 6 inches in diameter, Ed and Kate Coleman's Freke Bowls are made for function as well as display. With their shape and bright colors, they add an unusual twist to everyday activities.

“There are floor-to-ceiling windows in almost every room,” says Kaja Taft of her prefab home in Portland. “Light was a big part of why we loved this design.” With so much light comes the need to block it out at times, especially in the children’s rooms. Though the couple invested in solar shades and blackout curtains by Mari Design, “They still get up at 5:30,” Kaja says with a laugh. As in all the bedrooms, the carpet tiles are from Flor.

Triangular windows beneath the roof line are a common element in all of the second-floor rooms, including the master bedroom.

Outside, a triangular saltwater pool overlooks breathtaking views.

The triangular shape creates a volume that feels simultaneously cozy and open.

A triangular pool is also terraced into the landscape surrounding the pavilion-like house.

Taft Residence Floor Plan A Open Studio B Bedroom C Bathroom D Mezzanine E Laundry F Master Closet G Master Bathroom H Master Bedroom I Shed J Planter K Entry L Bar M Powder Room N Dining Area O Living Area P Kitchen Q Mud Room R Utility S Den T Carport

The cedar weatherboard ceiling in the living pavilion features triangular recesses for lightbulbs.

Black and white kitchen cabinets painted with a triangular pattern add a whimsical touch to this funky kitchen.

A Nova Scotia couple learn that although triangular homes may look simple, they can be devilishly complex.

In the rear, triangular window bay juts from the building's main mass.

“The house is a piece of origami made out of triangular shapes, which we then draped over the landscape,” says Arbel.

The house's triangle pattern is also visible in the skylight hovering over the double-height main space. The ceiling beams are designed to resemble a honeycomb..

The master bedroom is perched above the kitchen. Kovel designed the landscaping with Kitty Davis of LandCurrent and Glenn Nardelli of Pistils Landscape Design + Build.

The upper floor contains most of the living spaces, while the lower concrete level houses the entry room, a triangular office, and a laundry and storage room.

In a spare bedroom/playroom located in another section of the house, Berg played with juxtapositions of shapes, installing an oak-wrapped, triangular reading nook inset with a circular window.

The slate roof of the triangular 'A-House' contrasts with the Douglas fir clad rectangular body of the adjacent form. Exterior terraces wrap and connect the two building forms.

In Portland, Oregon, Jeff Kovel of Skylab Architecture designed a house for Kaja and Kristopher Taft using HOMB triangular modules he developed with Method Homes. HOMB also features a super-insulated building skin and a highly efficient mechanical system. Kovel designed the living room’s sofa as well.

The Hansgrohe sinks are paired with Duravit faucets.

Architect Espen Surnevik chose the American typology of the A-frame lodge because it is "both intimate in its width and monumental in its height, and represented something basic with its triangular shape."

“There was nothing here. Eight hours later, there was a house made out of triangles," says resident Kaja Taft.

The original ensuite featured an awkward triangular shower, and was, as Daniel recalls, “the size of a closet. It looked like a powder room.” Clever use of millwork redirected the light from the skylight away from the bedroom and into the bathroom.

Triangular panels, progressing from stainless steel to glass, help to underscore the illusion of motion.

The core of the glass-enclosed spiral stair is a hexagon, a reference to the moments in the floor plan in which six triangular modules are joined together to form the shape.

Since the photo shoot, the couple have placed a desk in the triangular window nook and use the perch as a workspace. “There’s just something about it that hugs you,” says Shelley. “I feel very focused and relaxed when I’m here.”

The couple’s son, Rio, pauses on the mezzanine, which leads to the bedrooms.

Urban Armor by Martyn Lawrence Bullard for Ann Sacks, from $57 per square foot The triangular metallic tile comes in brass, steel, and black finishes and nine- and 18-inch formats.

The triangular structural support system continues on the exterior.

A small triangular window punctuates the interior of the floating sauna.