Classical Tessellations and Three-Manifolds

Classical Tessellations and Three-Manifolds

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This unusual, richly illustrated book explores a relationship between classical tessellations and 3-manifolds. The space of positions of an euclidean, spherical or hyperbolic tessellation is a Seifert 3-manifold possessing one of three of Thurston's geometries. These manifolds are described in detail with an emphasis on their geometry. Classical tessellations for the spherical context are illustrated by colour photographs of minerals. A further set of colour plates depicts, for the first time, all 17 plane crystallographic groups in mosaics from the Alhambra of Granada (up till now it was thou...