目次

Divided SpheresWorking with SpheresMaking a PointAn Arbitrary NumberSymmetry and Polyhedral DesignsSpherical WorkbenchesDetailed DesignsOther Ways to Use PolyhedraSummaryAdditional ResourcesBucky’s DomeSynergetic GeometryDymaxion ProjectionCahill and Waterman ProjectionsVector EquilibriumIcosa’sThe First DomeNC State and Skybreak CarolinaFord Rotunda DomeMarines in RaleighUniversity CircuitRadomesKaiser’s DomesUnion Tank CarCovering Every AngleSummaryAdditional ResourcesPutting Spheres to WorkTammes ProblemSpherical VirusesCelestial CatalogsSudbury Neutrino ObservatoryClimate Models and Weather PredictionCartographyHoneycombs for SupercomputersFish FarmingVirtual RealityModeling SpheresDividing Golf BallsSpherical Throwable Panoramic CameraHoberman’s MiniSphereRafiki’s Code WorldArt and ExpressionAdditional ResourcesCircular ReasoningLesser and Great CirclesGeodesic SubdivisionCircle PolesArc and Chord FactorsWhere Are We?Altitude-Azimuth CoordinatesLatitude and Longitude CoordinatesSpherical TripsLoxodromesSeparation AngleLatitude SailingLongitudeSpherical CoordinatesCartesian Coordinatesρ, φ, λ CoordinatesSpherical PolygonsExcess and DefectSummaryAdditional ResourcesDistributing PointsCoveringPackingVolumeSummaryAdditional ResourcesPolyhedral FrameworksWhat Is a Polyhedron?Platonic SolidsSymmetryArchimedean SolidsAdditional ResourcesGolf Ball DimplesIcosahedral BallsOctahedral BallsTetrahedral BallsBilateral SymmetrySubdivided AreasDimple GraphicsSummaryAdditional ResourcesSubdivision SchemasGeodesic NotationTriangulation NumberFrequency and HarmonicsGrid SymmetryClass I: Alternates and FordClass II: TriaconClass III: SkewCovering the Whole SphereAdditional ResourcesComparing ResultsKissing-TouchingSameness or Nearly SoTriangle AreaFace AcutenessEuler LinesParts and T . 257Convex HullSpherical CapsStereogramsFace OrientationKing IcosaSummaryAdditional ResourcesComputer-Aided DesignA Short HistoryCATIAOctet Truss ConnectorSpherical DesignThree Class II Triacon DesignsPanel SphereClass II Strut SphereClass II Parabolic StellationsClass I Ford Shell31 Great CirclesClass III SkewAdditional ResourcesAdvanced CAD TechniquesReference ModelsAn Architectural ExampleSpherical Reference ModelsPrepackaged Reference and Assembly ModelsLocal Axis SystemsAssembly ReviewDesign-in-ContextAssociative GeometryDesign-in-Context versus ConstraintsMirrored EnantiomorphsPower CopyPower Copy PrototypeMacrosPublicationData StructuresCAD Alternatives: Stella and AntiprismAntiprismSummaryAdditional ResourcesSpherical TrigonometryBasic Trigonometric FunctionsThe Core TheoremsLaw of CosinesLaw of SinesRight TrianglesNapier’s RuleUsing Napier’s Rule on Oblique TrianglesPolar TrianglesAdditional ResourcesStereographic ProjectionPoints on a SphereStereographic PropertiesA History of Diverse UsesThe AstrolabeCrystallography and GeologyCartographyProjection MethodsGreat CirclesLesser CirclesWulff NetPolyhedra StereographicsPolyhedra as CrystalsMetrics and InterpretationProjecting PolyhedraOctahedronTetrahedronGeodesic StereographicsSpherical IcosahedronSummaryAdditional ResourcesGeodesic MathClass I: Alternates and FordsClass II: TriaconClass III: SkewCharacteristics of TrianglesStoring Grid PointsAdditional ResourcesSchema CoordinatesCoordinates for Class I: Alternates and FordCoordinates for Class II: TriaconCoordinates for Class III: SkewCoordinate RotationsRotation ConceptsDirection and SequencesSimple RotationsReflectionsAntipodal PointsCompound RotationsRotation around an Arbitrary AxisPolyhedra and Class Rotation SequencesIcosahedron Classes I and IIIIcosahedron ClassOctahedron Classes I and IIIOctahedron ClassTetrahedron Classes I and IIITetrahedron ClassDodecahedron ClassCube ClassImplementing RotationsUsing MatricesRotation AlgorithmsAn ExampleSummaryAdditional Resources