A Lake House Built on Mathematical Order

17 July 2026

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On a flat, treeless lot on Lake Austin, A Parallel Architecture implemented the client's love of mathematics as its organizing principle for an entire house.

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A Parallel Architecture

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Brittany Chevalier

Most sites hand an architect drama for free: a slope, a view, a row of mature trees. This one offered almost none of that. "It's a large, sunny square piece of land," says Eric Barth, co-founder and partner of A Parallel Architecture, describing the lot before the project began. It was a flat rectangle on Lake Austin with a single large tree on the property line and full western exposure, a serious liability in Texas heat.

The clients were a young family who had purchased the land after admiring another A Parallel project across the lake. They came to the studio with a fairly open brief: a typical residential program, generational flexibility for kids, in-laws, or nannies over time, and a clear entertaining side of the house, but few fixed design opinions. What they did bring was a client with a background in mathematics, and a genuine enthusiasm for using it as more than an interest on the side.

That enthusiasm became the project’s organizing mantra. Rather than treat the flat, featureless site as a purely functional problem to solve, the studio and client found common ground in mathematical order itself. An early idea, a mathematically derived pattern meant to move through the site like a river, became a series of trapezoidal pavers flowing across the landscape. A structural column grid based on powers of two, a Penrose-inspired path, a binary siding pattern: each grew out of the same underlying logic. “We were using math as inspiration for order in the house, versus, oh, it’s on a steep hill, so we need to do X or Y,” Barth says. “We were filtering every decision through the mathematical order we created.”

The site still shaped the plan in more conventional ways. The house wraps into a “U” facing the lake, giving the family privacy from the road and neighbors on either side, while a walled, Japanese-inspired courtyard on the street-facing side brings in light and transparency without sacrificing that privacy. The massing itself is used to block the harsh western sun, casting shade across a series of courtyards, including one built specifically around the lot’s single mature tree, with a skylight that looks directly up into its canopy.

Structurally, the house is a full steel frame with concrete floors, essentially commercial-grade construction, chosen so the mathematical column grid could be expressed on the exterior as what Barth calls an “outboard skeleton,” while keeping the floor and roof packages thin enough to feel light rather than heavy-handed.

That structure also carries the house’s most distinctive move: large glass walls on both sides of the central living volume can open completely, and motorized solar

screens drop down to turn the entire center of the house into a screened porch when the weather allows, keeping bugs out without closing the space in. None of it was added as a technology layer after the fact. “It’s not applied layers of technology to transform the house,” Barth says. “Every stick you see in that facade has a purpose that is twofold.” The same visual openness carries vertically too, with clerestory windows connecting the main level to the floor above, so a young family isn’t sequestered in separate wings.

“It’s not applied layers of technology to transform the house,” A Parallel's Eric Barth says. “Every stick you see in that facade has a purpose that is twofold.”

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Inside, that transparency posed its own challenge. Interior designer Mark Cravotta of Cravotta Interiors led the interiors on the project and treated the architecture's clarity as a constraint rather than a backdrop. "Water's Edge was our first collaboration with A Parallel, and the first of three homes I've designed for this owner," Cravotta says. "The architecture is a modern glass box, so we treated the interior as an exercise in restraint. The moves were simple and few, which raised the stakes on getting each one right." In the primary bedroom and living room, floor-to-ceiling cashmere sheers soften the glass and filter the light. Much of the furniture was designed in-house as well, "so the rooms would feel of a piece with the house," Cravotta says.

The hardest part of the project, Barth says, was mostly invisible: navigating the zoning overlays and restrictions that apply to Lake Austin’s premium lots, unglamorous work that has to be resolved long before design can begin. What follows from it, on any lakefront property, is a persistent balancing act between privacy and view, since passing boats have a clear sightline into a lakefront living room. For a homeowner starting a similar project, his advice is to get the entitlement and site work resolved first, and to expect that tension between privacy and transparency from the outset rather than be surprised by it later.

Explore Water’s Edge by A Parallel Architecture on ArchiPro, browse more residential projects built on challenging or unassuming lots, connect with architects and designers working across Texas, and discover the products and materials behind homes built around an idea rather than a view.