Structure of Molecular Water and the 3D Pythagoras Theorem

Abstract

Water ice crystals inherently embed in their shape complex hexagonal structures, emerging mostly due to the O-H bond angle 104.5 degrees being close to the 120 degrees found in hexagons. This article explores the possible integration of water molecules into a recently published mathematical architecture called the Universal Gear model. Already published in a mathematics peer-reviewed journal, the Universal Gear is an orthogonally-intertwined construct of Pythagoras theorem driven planes, that all together provide a perfect balance in terms of the three main equations governing three-dimensional existence: zero net sum of lengths, zero net sum of areas and zero net sum of volumes. Computer-aided Design shows how a group of (simplified and realistic) water molecules successfully integrate into the (regular and irregular) version of the Universal Gear. Interestingly the geometric pattern that emerges from the projected field of water molecules integrated into the Universal Gear is a structure already observed in monuments of ancient civilizations. The ambient conditions, in terms of pressure and temperature, where such a structure could appear is not yet known, requiring further research preferably using computational molecular dynamics.