WASHINGTON — Few outside the Beltway are likely to be familiar with Synetic Theater, though the voters of the D.C. area’s coveted Helen Hayes Awards know it well, honoring the theater with nearly 100 nominations in the past decade.

That anonymity may soon end. The company, which has quietly gained a reputation for grace and originality as the purveyor of a movement-based, wordless performance style that fuses theater, dance, acrobatics, mime, music and special effects, has recently begun parlaying its status as a critics’ fave into a growing operation that will soon encompass not only a new D.C. home base, but also extend to the troupe’s first international engagement.

After a decade of presenting shows at venues throughout the area, including the Kennedy Center and the Shakespeare Theater (and receiving valuable support from both orgs), Synetic is poised to take its local operations to the next level, unveiling its 2012-13 season Sept. 20 in a cozy new home in Arlington, Va.’s Crystal City section.

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In November, the company will take two past productions to Tlbisi, Georgia for a 10-day tour. The trip abroad is a milestone for Synetic’s fledgling tour operation, which has previously performed in New York, Massachusetts and Pennsylvania.

Another priority is the enlargement of the theater’s robust acting studio, which has trained more than 200 actors in its idiosyncratic style. The operation will soon offer training in theater direction and tech specialties as well.

It all marks an unusual level of success for a troupe whose work could, at first glance, seem like artsy niche fare. Credit the popularity of Synetic’s “Silent Shakespeare” series — 90-minute adaptations of the Bard’s most familiar works including “Hamlet,” “A Midsummer Night’s Dream,” “Romeo and Juliet” and “The Taming of the Shrew” — for boosting the brand.

“The power of nonverbal communication is very strong,” says Paata Tsikurishvili, who co-founded the theater 11 years ago with his wife, Irina. The duo moved to the U.S. during the 1990s from the Republic of Georgia, where each had been involved in theater.

Today they are busy onstage and off, with Paata operating as Synetic’s a.d. and chief exec, and Irina as resident choreographer when she isn’t performing the most physically demanding roles.

Tsikurishvili, who is also principal adapter of the largely classics-based repertoire, says Synetic embellishes his homeland’s physical theater traditions with an array of theatrical forms and multimedia techniques. The theater’s canon is well suited for domestic and international audiences because of its broad appeal and accessibility, he notes. “We speak an international language,” he says, simply.

Synetic’s increased attention to administrative issues, meanwhile, is spearheaded by the company’s board chairman Angela Fox, a Crystal City executive and theater supporter. She helped Synetic gain a three-year grant from local philanthropists Robert and Arlene Kogod to supplement other foundation support; in 2010, Synetic received a National Theater Company grant from the National Theater Wing.

Among Synetic’s most steadfast admirers have been the judges of D.C.’s annual Hayes Awards. In a region that supports some 60-plus professional theaters, Synetic is solidly in the top tier of recipients, with 92 Hayes nominations and 24 awards during the past decade. Its 2011 production of “King Lear” ranks as the single most honored play, with 15 Hayes noms, one or more in every relevant category. “Lear” won four awards.

The Hayes recognition is a frequent irritant to competing theaters that debate whether Synetic’s art form should be classified as musical, theater or dance. Tsikurishvili considers the company’s work to be all of the above.

Synetic’s new season will feature four new homegrown adaptations, starting with a modern take on the “Jekyll and Hyde” saga that will incorporate an array of multimedia technologies. Other new wordless productions will include “A Trip to the Moon,” a comedy based on the 1902 silent film by George Melies; and “The Three Musketeers.”

The season will also include Tsikurishvili’s adaptation of “The Tempest” as the newest work in Synetic’s “Silent Shakespeare” canon.

That, too, will be a step up for the troupe, with the story’s action to be played on a water stage and the house decorated like the eye of a storm. “It will be our edgiest, riskiest, and most expensive production to date,” Tsikurishvili says.