What child hasn’t dreamed of being big, of finally towering over Mom or Dad?

Most kids have to wait years to fulfill that fantasy — unless they visit the elegant 1907 edifice at Eighth Avenue and 14th Street. There, they can experience the Beuchet Chair: When viewed from a specific point, anyone standing next to the chair appears two or three times larger than someone seated in it. (This effect results from the eye’s perception of context.) Or they can explore the Ames Room, which looks like a cube but is actually a trapezoid: When two people stand at opposite corners of one of its walls, an observer will see one individual as gigantic and the other as tiny.

These attractions, named for the scientists who devised them, are among more than 70 at the Museum of Illusions, a space of about 4,500 square feet inside a building resembling a Greek temple. The interior, however, is more like Lewis Carroll’s Wonderland. Here, you can see visitors appear to shrink or grow, like Alice, or even lose their heads. The Queen of Hearts would love the “Head on the Platter” exhibit, a painless way — courtesy of mirrors — to become temporarily disembodied.

“I like to call us a reality-bending establishment,” said Renne Gjoni (pronounced re-NAY JONE-ee), chief executive of the Manhattan museum, which opened last September. Founded by Roko Zivkovic and Tomislav Pamukovic in Zagreb, Croatia, in 2015, the first Museum of Illusions was such a sensation that more than a dozen others are now bending reality in places like Shanghai and Kuala Lumpur. One is to open in Dallas this fall, “and we’re looking to open a couple more,” Mr. Gjoni said. The most successful is New York’s, which, he said, welcomes about 30,000 visitors a month. ( Admission is $15 for ages 6-13 and $19 for adults. )

Many of those entering are children, who can celebrate birthdays here as well as engage in hands-on activities. One of the newest exhibits, Escape 21, consists of a large tabletop whose framed surface is covered with colored wooden tiles. The object is to release one tile, the king piece, from the frame by sliding — but never lifting — those surrounding it. (It’s not an illusion but a brain teaser.) The museum also has a playroom with puzzles whose interlocking wooden pieces evoke Rubik’s Cube. Such mental challenges will intrigue those 8 or older, while spaces like the Tilted Room (it’s exactly that) or the Color Room (whose visual effects depend on spotlights in primary hues) can delight preschoolers as much as camera-happy teenagers.