Abstract
Class III hexagonal geometries are unique due to their chiral symmetry but the skew topology introduces additional computational complexity making their use in constructed shells rare. In nature though class III tessellations are very common at the microscopic level. In 2015 Kitrick [1] presented a general solution for deriving plane hexagonal tessellations applicable to Class I and II geodesic geometries. These classes are intrinsically symmetric and allow the solution to be resolved within the Schwarz spherical triangle. Class III geometries do not fall neatly within the Schwarz triangle and present an initial condition problem that is addressed in this paper allowing plane hexagons to be effectively derived for this unique class. Shells consisting of only plane hexagons offer advantages with respect to face and edges for both single and dual layer shells.
