At the base of Echo Mountain in Phoenix, a geometric home by Wendell Burnette opens up to the surrounding desert landscape. Photo by Dean Kaufman.

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

The planks inside the house blend into those on the small porch just outside. It's a nice touch that helps marry the outdoors with the home's interior.

The Baumann family residence in Gowanus, Brooklyn, is all geometry up front, with a rectilinear grid of steel and cypress comprising the structure’s double facade.

A geometric frame delineates the kitchen without closing it off. The island is an ideal spot to enjoy a casual breakfast.

Mint green-painted ironwork and tiles connect the indoors to the outside more fluidly.

A lone saguaro marks the southwest corner of Thomas and Laura Hyland’s property, which is situated adjacent to the Phoenix Mountain Preserve. The structure’s main living volume is elevated and faced in glass, overlooking a descending pathway that leads to a pool tucked into the site.

The geometric pool also captures views of the lush landscape.

The owners of this home selected a geometric-patterned glass tile backsplash by Island Stone. The glass tile keeps the space bright, and the pattern adds interest.

The winglike dips in the roofline situate and hold the house against the region’s brutal winds. As the outdoor chairs attest, lifestyles here pass easily between inside and out; a long hike and a good swim are always just steps away

Cedar slats help this Ontario lake house float soundly atop still waters. Photo by: Raimund Koch

Sebastian Heise’s wooden structure, seemingly atilt, overlooks a green valley in Oberwiesenthal, Germany. The two horizontal windows on the side and the front porch give the home its own unique sense of balance.

A look at the exterior of Tyler and Brown's new 2,150-square-foot house, located a stone's throw away from Tyler's mother's home.

By merging typical Saigon architectural and stylistic details, architect Toan Nghiem of a21 Studio created a space that brings family together. Stacking roof layers, open flowering balconies, and an alleyway that serves as a living room, dining room, and outdoor playground are all filled with colorful, rich materials. Inside Saigon House, reclaimed and second-hand furniture lend history and spirit to the home. With so many small interior rooms and divisions between spaces, the addition of a net ceiling brings openness to the back alleyway, where the family often gathers to eat dinner. Not only does the net allow for ventilation and light, but it offers a place to play for the children, who love to climb and lounge above their parents.

Outdoor corridors allow the Worples to walk through the house and across the cove without going inside.

This is Unit 4, the only one with a redwood dividing wall between the kitchen and the living room (the rest have open concrete islands).

The central inspiration for the Geobils was to start a personal creative challenge for Haley Ann Robinson. She wanted to branch out and try working with totally unfamiliar materials.

Evidence of Robinson's popular wooden rocks are echoed in the simple wooden and ceramic beads that hang on many of the Geobils.

Robinson has only ever dabbled in jewelry-making (though "not for a while and not for long when it lasted"), though she likes the idea of her Geobils being thought of as "wall jewelry."

After splitting her time between Los Angeles and Portland—and repeatedly returning to the Northwest for inspiration—Robinson has finally set down roots in the city that fuels her many projects.

Through her side projects, Robinson can explore three dimensional projects that require her to "get messier" than her daytime work as a graphic designer. "I love creating with my hands," she says, "and being a graphic designer I sometimes get lost in computer land."

The headboard in Hansen’s bedroom echoes the 2013 side-board. The wallpaper is from Arte.

Furniture with emphasized linear elements helps prevent the appearance of clutter in small spaces. It's particularly effective when highlighted in playful colors like the blue bench storage rack in this London guesthouse. Photo by Ben Anders.

The geometric front facade of the home is made of Cor-Ten steel, segregated into eight vertical panels. Juxtaposed with its lush natural environment, the front elevation is a minimal and abstract counterpoint to its surroundings. An exterior pool meets the facade at its base.

Inside the studio

Krisel was also known for his boldly modern approach to landscape. The Menrad residence, shown here, features a distinct geometric design. The architect, working in the harsh Palm Springs climate, relied on hardscape elements—setting a precedent for drought-tolerant landscape design.

Transience mirrors by Dutch design collaborators David Derksen and Lex Pott is a groovy geometric piece that exhibits the absolute beauty of the oxidation process, resulting in a an elegant formation of hues and pattern.

Cubes Rug by Paul Smith for The Rug Company. Smith looked to stained glass windows for this abstract take on the ancient art. He also used a special looping method to create crisp edging.

"Residential | repetition"

The dining table is from French retailer AM.PM., the pendants are by Him + Her, and the shelves are by Tomado Holland. An Ikea rug echoes the geometric motif found throughout the apartment.

In the living room, Hansen’s convertible Night couch and coffee table join a Black Marble rug by Suki Cheema and Slovenian Bear from Charles Fréger’s Wilder Mann series.

Shine a Light Benshetrit’s table lamp, for the lighting and furniture company .MGX by Materialise uses QuaDror’s infinitely scalable geometry to create a honeycomb of 1,200 modules that fits over a metal base holding a 40-watt halogen bulb. The lamp, which arrives flat and expands, accordion-like, when lifted, is manufactured via selective laser sintering (SLS), a 3-D printing process that uses a laser to solidify layer upon layer of powdered resin particles. “When you buy the lamp, you get a disc with the file on it, so if it breaks, you can ‘reprint’ it,” Benshetrit says.

Unlike your typical sawhorse desk, which often comprises a pair of struts and a board as the desktop, the QuaDror system can support a much sleeker aesthetic.

Compact Desk “Designers always like the idea of sawhorses for desks,” Benshetrit says. “They’re cheap and easy to move, multiply, and put away.” The QuaDror version has a slightly smaller footprint than a standard sawhorse, which means more lateral leg room, “and if you orient the V side of the triangle toward where you’re sitting, it’s even roomier.” Additionally, “it folds flat, doesn’t require assembly, and works with any desktop.” Studio Dror plans to self-market the desk, first on the Web, then through selected stores, and to hit different price points depending on the quality of the wood. “I like the Johnnie Walker approach—birch is Red Label, mahogany is Blue.”

Whimsical figurines are on display in MacIsaac's home.

"A lot of people were skeptical about the idea, even though it wasn't the first time I pulled off something crazy," Cadena says. "I just trusted my intuition and the philosophy of the chef."