# Twice Spun¶

Hactar, 2024-04-15

One day Acolyte Quenta found herself wandering the gardens, as she often did, and upon crossing a small bridge she came upon a curious puzzle. It appeared in the form of an ordinary 3x3x3, but with an odd coating on the stickers that presented a gradient over each piece that tilted strangely as she observed it from different angles. She took the cube and scrambled it, intending to return it once she had solved it.

As she twisted the puzzle, she became sure that it was playing tricks on her. Even whole-puzzle rotations seemed to behave oddly. She had placed a blue piece next to an orange piece, but upon spinning the puzzle in her hands, the blue piece became orange and the orange piece had become blue! After struggling for a half-hour, managing only to pair a handful of pieces, she resolved to find Master Eiji, who was an expert in variations of the 3x3x3.

Upon showing the mysterious puzzle to Master Eiji, he led her inside to a bare room with a column in the center. “Walk around the column and return to me. Then you shall learn how to solve this puzzle,” he instructed. Quenta gave him a quizzical look, but then walked around the column– and found that Master Eiji had disappeared! Furthermore, the room was slightly different; she could not see the entrance they had come in from, and instead there sat a bench against the wall. She walked another full circle around the column, and then found Master Eiji.

“Master Eiji!” she exclaimed. “What strange geometry is this room constructed from? It is neither Spherical nor Hyperbolic, as the light does not seem to bend. But it cannot be Euclidean, because I circled the room twice before returning to you–” she stopped.

At that moment, Quenta was enlightened.