You can see plenty of fine dance programs, but you’ll not often find one with a great concept behind it. This was the mark of sophistication that Pilobolus brought to Wolf Trap in its enthralling and frequently astonishing performance Tuesday night. It was a deeply satisfying presentation, because of the guiding idea woven throughout.

The idea here was how mystery prevails even in the face of absolute transparency. We’ve got nothing to hide, this troupe told us, in dispensing with such theatrical conventions as curtains. The dancers were on stage warming up as the audience filled the Filene Center and spread out on the lawn. The stage crew mopped in plain view while we watched a brief video of the slippery grace of microscopic critters, a nod to the dance company’s namesake, an energetic barnyard fungus.

Warm up, set up, human bodies: Nothing magical here. This was the pattern — and the joke — throughout the evening. In between the five dance pieces, we were treated to short, quirky videos (exploding cans of cabbage; a child’s face imperceptibly, eerily aging) while the crew prepared the stage. The joke (and the miracle) was that once the dancing started, the effect was transporting and even transcendent.

Take the first and newest piece, “On the Nature of Things,” created this year. The title comes from the 2,000-year-old Roman poem “De Rerum Natura” by Lucretius, who argued that physics and chance governed the world, rather than frightening godly powers. Pilobolus doesn’t seem to agree. Or maybe it sees humans as gods. Surely that’s the way the audience saw Benjamin Coalter, Jordan Kriston and Nile Russell, the heroically muscled, nearly nude dancers.

If the small circular platform on which they wrestled was their earth, their bodies were full of heavenly yearning. They seemed buoyant, almost helium-filled, as they climbed atop one another with uncanny ease, in slow motion, always reaching up, almost soaring then melting downward as another rose up atop someone’s shoulders or back, propelled from below in ways cleverly hidden from us. You never saw the next move coming.

From Pilobolus's “On the Nature of Things.” (Handout/Robert Whitman)

There was a Sistine Chapel esthetic here, in the fleshiness, the impressive musculatures and the dancers’ magical floating quality, all enhanced by Neil Peter Jampolis’s golden lighting. But just as you’re thinking that the nature of things involves core strength and good friends, a power play erupts, and one dancer throws the other two off. He rises godlike before us, beautiful and cruel.

If you think of Pilobolus as the commercial eye-candy whose silhouetted trompe l’oeils have been used in car and Super Bowl ads, this program returned the group to its artistic origins. Or rather, the group has found a way to expand on them with inventiveness and complexity that is also wholly entertaining. In “All Is Not Lost,” the dancers re-created their Grammy-nominated 2011 music video with alt-rock band OK Go. Wearing seafoam-green jumpsuits, they slid along the clear surface of a high platform; we could watch them in the flesh or watch a live video of them, shot from a camera underneath the platform. The choreography worked both ways: as the rhythmic interaction of bodies (live), or as the amazing, kaleidoscopic pattern of bare feet and green limbs (on the video), their soft tissues flattening and squishing like bugs on a windshield, or specimens mounted on a microscope slide. There was that fungus idea, again.

A collaboration with comic illusionists Penn and Teller resulted in a work titled “[esc],” the evening’s corker, where dancers turned into escape artists, padlocked into a crate, stuffed into a duffle bag or handcuffed to a stripper pole. Not only did they emerge, but they did it with a sexiness and musical verve to put their collaborators out of business. AC/DC’s “You Shook Me All Night Long,” which accompanied the two-man handcuff-escape that turned into a homoerotic display of acrobatic power, could have been the evening’s anthem. We had seen how tightly the chains bound the men. All was transparent. Yet nothing was transparent. The mystery and majesty of the human body was the message here, down to the last beat.