Spherical ModelsWell known through the work of Buckminster Fuller, models of spherical polyhedral excite the imaginations not only of mathematicians, architects and engineers but also of artists and designers. This book, concerned with polyhedrons, sphere tilings, and dome structures, offers a well-illustrated, practical approach to creating a host of beautiful and interesting models, including starfaced spherical forms that can serve as basic structures for geodesic domes. Employing only the most elementary mathematical principles, the text initially provides complete instructions for making spherical models from five regular solids, using only circular bands of paper, a ruler and a compass. Also discussed is tessellation, or tiling, on a sphere and how to make spherical models of all the semiregular solids. The volume concludes with a discussion of the relationship of polyhedral to geodesic domes and directions for building models of the domes. Abundantly illustrated with photographs, drawings, and computer graphics of attractive geometrical models, this volume will appeal to a wide range of readers—from students and teachers of mathematics, art, design, architecture and engineering, to recreational mathematics enthusiasts and builders of geodesic domes. |
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4-frequency a b a arc lengths arc measures arcs bands bisector calculated central angles chord factors circle circular bands circumscribing sphere completed model construction cuboctahedron cumscribing sphere derived dodecahe dron dual edge length edge models equilateral triangle Facial planes Figure find first five flat follows frequency geodesic domes geometry given Gnomonic projections grid segment hedron hexagons hexagram icosahe icosahedral face inscribed isosceles triangle Layout linear measures mathematical measures and bands method needed nolids octagram paper bands penta pentagon face pentagrams pentakisdodecahedron Photo Plate polygons polyhedral radians radius Reflections regular and semiregular regular spherical models Rhombicosidodecahedron Rhombicuboctahedron right angles semiregular polyhedrons shown in Fig shows small stellated dodecahedron smaller triangles Snub cube snub dodecahedron spherical cube spherical icosahedron spherical trigonometry square stars tahedron templates tessellated network tessellation tetrahedral three regular spherical tion triangle face triangles omitting Truncated cube Truncated dodecahedron Truncated icosahedron Truncated octahedron Truncated tetrahedron uniform polyhedrons