When a giant cube visits a little 2-D town, a creature named Gomez gains the power to see his flat world in a whole new dimension.

The hexahedron spouts a few lines in an unknown language, plops a small red cap onto Gomez’s head — the fez of “FEZ” — and vanishes, leaving Gomez with the ability to rotate nearly any room or environment he visits along its X-axis in 90-degree increments.

Each angle of view becomes a flat rendering of whatever objects are in it, and Gomez can only reach what he can see — if a door is on the far side of a building, you’ll have to rotate the world two ticks over to reach it.

Guided by a rainbowcolored tesseract called Dot, Gomez wanders the newfound depths of his world in search of golden cubes (found whole and in sets of eight pieces) — the fragments of the hexahedron, which shattered after imparting its power to Gomez. Collecting enough cubes opens up doors to new areas. There are no enemies, and if Gomez falls too far or otherwise meets a bad end, he reappears unharmed nearby.

Gomez can jump and climb along platforms, ladders and coverings of ivy, which is frequently found wrapped around buildings and objects. But to get to many hard-to-reach places you’ll have to manipulate the game world so a platform lines up just so, or an obstacle becomes a foothold.

It’s a very clever mechanic, and the cryptic clues and spare instructions leave much for the player to figure out when it comes to progressing through the trickier challenges of the game, though a map tracks which areas you’ve cleared of cubes and scoured for secrets already. And there are deeper puzzles to solve — for example, the strange letters the hexahedron speaks at the beginning and which are found in various places around the world of “Fez” correspond to our own alphabet.

The game’s visuals are in a pixelated style that evokes games of the 1980s, like “Super Mario Bros.,” and the indie darling “Cave Story.” The music and sound effects are effective and atmospheric.

For all its seeming simplicity, the game seems to struggle at times to deal with the rotations of the world as you navigate through it, and there are reports of other glitches in the game as well.