Catalog of geodesic hexagonal/pentagonal tessellations • These components provided to serve as modeling foundations for geodesic domes in your designs • Division of Icosahedron • Class I, II and III tessellations • Range of frequencies • Only certain triangular tessellations of the icosahedron conform to hexagonal groupings • Endpoints optimized on the surface of a sphere, using an electron-charge repulsion algorithm (search online for "Thomson problem") • A map is provided for each sphere, depicting icosahedral-face tessellation • Note that Class III tessellations exhibit various degrees of twist, or 'skew' to the faces • Class III tessellations are also 'chiral,' meaning the rotated symmetry can be either right-handed or left-handed • This model only shows one direction of twist • If you need the opposite twist, SketchUp's 'scale' tool can be used to mirror the sphere • Spheres are 1-foot radius • Use the SketchUp 'scale' tool to increase to the dome size desired • See cross-reference model, "Geodesic Catalog • Tessellation" for definition and derivation of classes and frequencies: #Buckminster #Bucky #dome #Fuller #Geodesic #geodesic_dome #icosahedron
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