Rotegrities • Pentagon Scale

Rotegrities • Pentagon Scale

TaffGoch
This model depicts the variation in the size of "nexo-rotegrities," when the band length from the smallest rotegrity is used to size the pentagon bands for the other seven nexo-rotegrities. <i>(Essentially, the pentagons are all the same size)</i> Each arc is <u>equally</u> subdivided, by three, at the intersections. The model also includes a <i>(hidden)</i> geometry layer that contains the 3-line-segment arc sectors employed during construction. This layer makes the equivalent 3-segment subdivisions readily apparent. For a preview image of this layer, see: <a href="http://taffgoch.deviantart.com/art/Nexorades-pentagon-scale-ARCS-628884200">Nexorades pentagon scale - ARCS</a> _________________________________ "Rotegrities" are also commonly referred to, today, as "nexorades." This set depicts the first 8 "nexo-rotegrity" spheres, in order of increasing triangle density <i>(i.e.; frequency)</i> 1v{0,1} • Radius = 1.000 <i>(The first rotegrity, introduced by Richard Boyt, 1970)</i> 2v{1,1} • Radius = 1.803 <i>(Class-II geodesic tessellation)</i> 2v{0,2} • Radius = 2.141 <i>(Class-I geodesic tessellation)</i> 3v{1,2} • Radius = 2.965 <i>(Class-III geodesic tessellation)</i> 3v{0,3} • Radius = 3.411 <i>(Class-I geodesic tessellation)</i> 4v{2,2} • Radius = 4.079 <i>(Class-II geodesic tessellation)</i> 4v{1.3} • Radius = 4.279 <i>(Class-III geodesic tessellation)</i> 4v{0,4} • Radius = 4.843 <i>(Class-I geodesic tessellation)</i> <i>(The frequency designations, above, follow current standards for geodesic sphere/dome labeling)</i> #buckminster #frame #fuller #geodesic #nexorade #reciprocal #rotegrity
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