Ever hear of the Haberdasher Puzzle? In 1903, a mathematician named Henry Dudney published a paper showing how an equilateral triangle divided into four pieces could be reassembled into a perfect square.

Eighty-four years later, a designer named Maty Grünberg stumbled onto Dudney’s geometric discovery, which Grünberg then used as a blueprint for a table he designed that could be rearranged into eight separate configurations.

That idea seeped into the unconscious of Maty’s son David, who as an architecture student in 2008 completed his dissertation by developing a prefabricated house that could withstand extreme subarctic temperatures by, in essence, moving with the sun.

Now, as director at D*Haus, a London-based architectural firm that was formed about a year ago, David Ben Grünberg and his partner David Woolfson are pushing architectural boundaries with their Dynamic D*Haus, which they say has been "inspired by the poetics found in logic and geometry." Dynamic D*Haus can adapt to its environment by literally “opening up” so that external walls unfold into eight different shapes, allowing glass internal walls to become facades. One goal is to expose this shape-shifting house to as much sunlight available at a given time, day, or month.

The design of this factory-manufactured house, at roughly 1,100 square feet, includes two bedrooms, an open living room (that theoretically could adapt to changing family sizes), and a bathroom.

Woolfson points out that the largest part of the house doesn’t actually move, so installing a kitchen wouldn’t be a problem. The bathroom could be positioned at a “hinge point” within the house between the bedrooms.

The partners are still working on what would drive the motion of the house, but the foundation probably will be on some kind of a sliding track system. The external walls would be made from a translucent insulating material that forms a waterproof membrane and eliminates the need for an insulation canal behind the walls.

This house won’t be cheap. A full-sized model excluding land is expected to cost 1.2 million British pounds, or $1.9 million, although the partners envision a simpler model that could lower the price to the equivalent of $600,000.

While the concept for D*Dynamic originally was devised to address the severe climate of the Lapland region in Finland, the company’s partners believe their house also would be applicable in the colder areas of North America.

A prototype, cut from DuPont Corian, was on display at the Anise Gallery in London in November. The partners, who are self financed, hope to have their first real house built within the next two years (the location has yet to be determined) and were planning to use the website Kickstarter to drum up capital for the project.