Interior geometry reconstructs the sarcophagus envelope and exterior slope of the Great Pyramid of Khufu

Abstract Preserved architectural geometry can constrain the missing form of a damaged object. We derive a reversible relation linking the sarcophagus, King’s Chamber and exterior profile of Khufu’s Great Pyramid. In a centred chamber section, equating a crossed-line rise to each lateral gap reconstructs length and profile angle from three preserved interior dimensions, without a fitted continuous coefficient. Petrie’s measurements yield a 2.303-m envelope and a 51.838° profile, differing from his historical comparisons by 1.69 mm and 23.7 arcsec. The relation alone matches length within 0.2% among 127 declared rule classes and retains the best central length fit in expanded rule families. An additional volume constraint also recovers sarcophagus height. Architectural context thus supplies a quantitative constraint on lost form, with explicit predictions for independent surveys of the damaged ends and original position.