A More Realistic Solution to Refugee Housing Using the Isoperimetric Honeycomb Conjecture

Abstract

Over 6.6 million people live in refugee camps around the world. High-velocity wind storms frequently rip short-term structures in these camps apart, destroying what little refugees have left. Through the application of the Isoperimetric Honeycomb Conjecture and the Laws of Phi, we engineered a new, translationally symmetric icosahedron. This design minimizes the use of material needed by maximizing the number of isoperimetric hexagons and minimizing the number of pentagons while still creating a dome-like structure. After aerodynamic testing, we found the wind resistance of our structure to be 174.67 mph. Additionally, we engineered inexpensive, waterproof connectors to securely hold the structure together. These connectors were designed by developing a novel mathematical method involving calculating each dihedral angle using multivariable calculus and Euclidean geometry. We used three-dimensional vectors to calculate each cartesian point, then using the cross product found the normal vectors of each vertex. The point of intersections of these normal vectors were then inserted into an inverse cosine function giving us the dihedral angles needed for the connector design. This mathematical method was proven through the construction of our life-size model. The final 5-6 person structure is waterproof and fire-resistant, lasts 20 years, folds to the size of 1 backpack weighing 28.9 lbs, and costs $58.11 to make, which is 400-500 dollars cheaper than anything comparable on the market today. Also, our house follows the laws of special right triangles and therefore can be as small as a 1-2 person house or as big as a temporary hospital or school without additional structural support. The efficient, secure design, combined with the wind resistance of the structure, can help millions of refugees and has applications to help others such as military personnel or victims of natural disasters.