Foreword by Arthur L. LoebPrefaceIntroduction: Basic properties of the sphereI. The regular spherical modelsThe spherical hexahedron or cubeGeneral instructions for making modelsThe spherical octahedronThe spherical tetrahedronThe spherical icosahedron and dodecahedronThe polyhedral kaleidoscopeSummaryII. The semiregular spherical modelsThe spherical cuboctahedronThe spherical icosidodecahedronSpherical triangles as characteristic trianglesThe five truncated regular spherical modelsThe rhombic spherical modelsThe rhombitruncated spherical modelsThe snub forms as a spherical modelsThe spherical dualsSummaryIII. VariationsRegular and semiregular variationsStar-faced spherical modelsIV. Geodesic domesThe simplest geodesic domesGeodesic domes derived from the icosahedronGeneral instructions for making geodesic modelsAn alternative method of approaching geodesic segmentationIntroduction to geodesic symbolism and classificationGeodesic models derived from the dodecahedronAn alternative for geodesic segmentation of the dodecahedronA second alternative for geodesic segmentation of the icosahedronAn alternative for geodesic segmentation of the snub dodecahedronA third alternative for geodesic segmentation of the icosahedronFinal commentsV. Miscellaneous models"Honeycomb models, edge models, and nolids"An introduction to the notion of polyhedral densityEdge models of stellated formsSome final comments about geodesic domesEpilogueAppendixReferencesList of models