Sum of Interior Angles

The corridor, once a stable, comforting pathway of polished obsidian, now pulsed with an unsettling tremor. Elara pressed her palm against the cool, smooth surface, feeling the subtle vibrations travel up her arm. Chapter 11 had ended with a blinding flash of light and a dizzying sensation of displacement, and now she found herself standing before an obstacle of truly monumental proportions.

Before her loomed a door, not of wood or stone, but of interlocking, crystalline geometric shapes. It was vast, easily twice Elara’s height, and utterly impassable. Embedded in its center, where a handle might have been, was a complex dial, a mosaic of smaller polygons, each a different hue of the spectrum. Around the dial, etched in glowing script that seemed to shift and reform as she watched, was a single, daunting phrase: "The sum of the interior angles shall set you free."

Elara’s heart hammered against her ribs. This was it. The labyrinth wasn't just a maze of corridors; it was a series of intricate puzzles, each one a test of her understanding. She’d mastered the sine wave, danced with the cosine, and teetered on the tangent’s edge, but this… this felt like a foundational challenge.