Compression is nature’s glue. Case in point: the Armadillo Vault, a self-supporting pavilion comprising 399 limestone slabs and spanning 52 feet, curving and bending around the columns of a 13th-century Venice building at this year's Architecture Biennale. No glue, no mortar, no hidden substructure to ensure the 24-ton edifice doesn't collapse—just really smart architecture.

At the heart of what architects and the engineers who work with them do is the opposition between compression (pushing together) and tension (pulling apart). The Eiffel Tower, the stone-clad cathedrals of Europe, every bridge ever—they all rely on balancing these two forces.

The Armadillo Vault goes a different direction. Because its limestone blocks form a series of conjoined arches—a classic form that turns compression into strength—it stands with only a minimalist system of tension ties that helps balance the structure at the ground level. That's not to say it doesn't need a little help. “There’s no way to imagine this kind of shape without computation,” says Philippe Block, director of the research group at ETH Zurich that developed the Armadillo Vault.

A few years ago, the Block Research Group created a software package called RhinoVAULT, designed to let architects manipulate tension and compression forces within a 3D model. That's what let them design the Armadillo; because it's inside a world heritage site, the Corderie dell’Arsenale, the team had to redistribute the forces on the floor to have as minimal a footprint as possible. The undulating shape of the final design is what the software came up with, and it's both functional and aesthetic.

To build the pavilion, masons followed the RhinoVAULT results to assign the blocks, from a West Texas quarry, numbers and specific locations. Then they built a wooden form inside the pavilion and laid the stones in place atop it—two-inch thick pieces at the top, and five-inch thick pieces near the bottom. Remove the scaffolding and the stones support themselves. “You can almost not put a razor blade between the stones,” Block says.

And the thing is pretty tough. Block says a football team could dance on top of it—"an American football team," he clarifies. Walking inside, visitors can look up and see the forces acting on the blocks etched into the ceiling, a visual representation of the physics that the Armadillo Vault relies on and proof that the flowing, sinuous forms of buildings from architects like Zaha Hadid and Frank Gehry don't need complex steel substructures. Block says design tools like RhinoVAULT could let them build the same elaborate structures with far less material. “It’s a more honest representation of a geometry,” Block says. “I think it’s also going back to showing what materials can do—even humble materials." The fact that those materials can also be beautiful is just a bonus.