Read here about the application of tensegrity principles to tents.
A tent is a shelter consisting of fabric or other material draped over or attached to a frame. First used as portable homes by nomadic peoples, tents are now more often used for recreational camping and temporary shelters.
There is no known commercially produced tent that conforms with the strict definition of tensegrity. However, there are many tents that have some aspects of tensegrity. The remainder of this article discusses those tents.
Closed vs. Open Tensegrity Systems
What exactly is tensegrity in commercial tents, which are largely fabric tensional structures that require external support? We argue that addressing tensegrity in the context of commercial tent production is in agreement with our goal of advancing tensegrity research, implementation and comprehension. However, to do so we need to differentiate between open and closed tensegrity systems.
A closed tensegrity system is a self-sufficient array of struts and tendons, arranged in such a way that the struts and tendons enforce an ongoing structural integrity in the overall assemblage. An open tensegrity system is an array of struts and tendons that enforces an ongoing structural integrity that participates within, and depends upon, an external system.
Tents in Tensegrity Literature
The tensegrity literature to date considers closed tensegrity systems as being tensegrities, although Fuller advocated a broader view.
Burkhardt wrote, "A circus tent ... is a non-self-sufficient tensegrity. It is anchorage dependent. Here we're imagining poles which are not rigidly attached to the ground which are held in place by tent fabric and ropes which are staked into the ground. Without the purely-tensile components, the whole thing would fall over. Camp Elsewhere's Tensegrity Shade Structures fall in this category. Other tent strategies would need to be examined on a case-by-case basis." 
Writing about a shade structure, Gómez Jáuregui pointed out that it has no “self-equilibrium stability since it needs to be anchored to the ground in three points and the struts are not stable if they are not resting on the ground” and because “the absence of prestress is definitive to deny the denomination of tensegrity to this shadow roof.” 
However, Burkhardt also wrote a broader definition: “a tensegrity is a pattern integrity which has purely-tensile portions which are essential to its integrity.” In this broader phrasing Burkhardt writes in the spirit of Buckminster Fuller, who wrote “All structures, properly understood, from the solar system to the atom, are tensegrity structures.”
Commercial tents have functional requirements, such as a wide floor area and anchorage requirements, that forbid truly self-sufficient design. A tent designer wrote, "I could easily make the structure self-sufficient... but that would defeat its utility as a tent, as the floor wouldn’t be flat and it could blow away." 
That said, one can assess whether a given tent has more or less tensegrity in its subsystems. A pup tent, for example, maintains the tension of its fabric walls by using poles and stakes to enable the Earth itself as an anchorage. In the pup tents struts and tendons, there is not a single subsystem that can be considered as self-structuring.
In contrast, in a ring strut tent such as the Ring Pole™, the subsystem of thin compression ring struts acting with narrow fabric tendons is a subsystem that clearly is structured on tensegrity principles.
Howe Design Membrane Tensegrity Tent Prototype
The prototype pictured below was developed by Howe Design Group for Sierra Designs in 1996. The complexity involved in assembly prohibited further commercial development, and the project was shelved. However, the principles were applied to later commercial tents such as the Sierra Designs Tensegrity 1 .
Pole Supported, Ring Strut Tensegrity Tents
Ring Pole™ tents are open, in that they depend on a central pole, affixed to the ground, elevating via compression the center of the tent. Ring Pole™ tents which use a Trussring™ support system consisting of a shelf (the truss) and a hoop (the ring).
Ring Pole™ tensegrity tents are tensioned fabric structures that use a patented support system; thin compression rings float in the canopy and are retained by narrow fabric shelves giving the tents girth where it is needed -- at head height. A center pole pre-stresses a tensioned canopy which is shaped by floating compression rings and staked to the ground. Trussring™ tents represent a new tent type; they are not dome tents, wall tents, tunnel tents or pyramid tents. The top cone and truncated lower cones have taut anticlastic surfaces. The compression rings are sectioned and shock-corded together for ease of folding. In strong winds the compression ring sections rotate in relation to each other to dissipate shear stress.
This large double-hoop 8 foot tall tent uses a lower hoop that is made up of hollow aluminum tubing.433 inch in cross-section, roughly 40 foot long and 12 feet in diameter to define, in conjunction with the upper hoop, a huge living space. The foot print is 225 sq. ft., this tent weighs 18 pounds and sets up in about ten minutes. The hoop acts like a noodle outside of the tent but when it is in place and the tent is pre-stressed it barley budges when pushed laterally. It is unlikely that a large and narrow hoop like that could provide such structural utility while isolated in a field of tension without principals of tensegrity being invoked.
This type of structure resembles the Killesberg Tower. That is described as a prestressed cable-net structure. Link: http://www.sbp.de/en/build/sheet/11-Aussichtsturm_Killesberg.pdf
Shelter-systems claims that the Diamond DomeTM is a tensegrity structure. However, the structure is completely anchorage dependent. Poles of wood or bamboo are fitted into plastic caps, outlining four square panels that are anchored to the ground. The only tension is in the fabric stretched within the four square windows. Tension plays no role in the structural cohesion of the structure.
Link: http://www.shelter-systems.com/diamond-dome1.html%7Cthumb%7C500px%7Cnone%7CDiamond DomeTM shelter-systems tent.
Sierra Designs Tensegrity I
In 1998 Howe Design Group designed and produced a prototype named the "Sierra Designs Tensegrity 1 experimental tensegrity tent."
In the September 1998, popular mechanics published a two page preview of the Tensegrity I tent by Sierra.
From the article: Sierra Designs has compressed the tensegrity principle into an arch--a slice of intersecting triangles that are integrated into the roof of the tent. The compression elements are hollow aluminum tubes that never bend, and the tension elements are shock cords run through the middle of the tubes. The arch takes the place of traditional tent poles. And since none of the 12 sections of tubing is longer than 19.5 in., the all sit neatly inside the folded tent. In order to pitch the tent you just slide the tubes along the shock cords until they connect. Then you stake down the sides of the tent in a prescribed order and it snaps to form. Tighten down the toggles and you have a perfect dome tent.
Sierra Designs Tensegrity 1 Tent
In 2014 Sierra Designs, in honor of the company’s 50th Anniversary, created a new Elite Collection of gear. This lightweight yet high performance line of products includes everything from rain gear to tents and sleeping bags, all reflecting the brand’s new unconventional approach to design. Part of this collection are two tents named "Tensegrity". Similar in style to the Sierra Designs MSR FlyLite tent, the non-freestanding Tensegrity tent ditches the majority of poles in favor of using your trekking poles as support instead. One small pole for the foot area and seven tent stakes ensure this tarp tent offers enough interior space and remains stable in inclement weather. Wider at the top than at the bottom, it adds a bit of extra space at the head and shoulders without the added weight of a more uniform footprint. The Tensegrity Elite tents use a silicone treated 20D nylon ripstop in the floor and body—the tent owner needs to do his own seam sealing. The Tensegrity instead features large drop doors that give an open, airy feel and tons of ventilation, while 12” awnings provide abundant sun and rain protection. A small gear closet at the back of the tent can be used to keep your packs out of the rain or rolled up for nighttime star-gazing.
The Sierra Designs Tensegrity comes in a 1 Elite version (1lb, 10oz; 17.1 sq ft interior) and 2 Elite version (2lb, 2oz; 29.3 sq ft interior). The tents are also available in two beefier (Feather Light) versions featuring a 30D nylon ripstop floor, 20D polyester ripstop body, and seam taping throughout—the Tensegrity 1 FL (1lb, 15oz; 17.1 sq ft interior) and the Tensegrity 2 FL (2lb, 8oz; 29.3 sq ft interior). The FL build uses 30D floors and 20D Flys with a 1800mm (fly)/3000mm (floor) PU coatings, fully taped. The ELITE versions use 20D nylon impregnated with Silicone (1400mm (fly) /3000mm (floor) and are not taped. The ELITE tents do not meet CPAI-84 fire retardancy standards and will not be available in states that enforce that standard. They also require user seam sealing. But they also have 4 times the tear resistance, dramatically improved UV resistance, and by eliminating urethane and the associated toxic FR chemicals, they eliminate the main fabric failure point and will truly last a lifetime with normal care.
Links and References
 Gomez Jauregui, Tensegrity Structures and their Application to Architecture, Page 91.
 Richard Webster, personal email, 6 April 2012