”Folds leave scars,” says Ilana (Kellie Overbey), the unkempt, divorced, slightly agoraphobic origami teacher at the heart of Rajiv Joseph’s terrific new play Animals Out of Paper. But instead of an inanimate piece of paper, she’s referring to her own past. After a surprise visit from high school calculus teacher Andy (Jeremy Shamos), she is thrust back into the world of Japanese paper-artistry via his prized pupil, Suresh (Utkarsh Ambudkar), a B-boy whiz kid recovering from his mother’s untimely death. He also happens to rock out some seriously ingenious origami — and he does it completely from memory, which goes against Ilana’s more rigid approach. The trio develops into a rather unlikely family.

Instead of devolving into Afterschool Special pathos, Joseph’s carefully modulated play slowly reveals darker edges to these characters. Ilana and Suresh share the bond of abandonment; and even Andy, a relentlessly cheerful fellow, keeps a running tab of blessings in a journal.

The performers give such rich, generous portrayals that the folds in the production barely show: Ambudkar is appropriately charming and anxious as the iPod-obsessed, broken teen; Overbey (The Coast of Utopia) has the best role of her career to date, twisting Ilana’s testy defiance into myriad emotional tones while still appearing utterly winning. And Shamos, currently the most unsung, consistently riveting actor in New York, is incapable of a dishonest move. His Andy could have easily been a wormy creep, but he peers right into the heart of this man. Just watch how he affectionately looks both Ilana and Suresh in the eye in every scene. He literally makes your heart ache. (Tickets: 212-246-4422) B+