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Generators and relations for discrete groups
1. Cyclic, Dicyclic and Metacyclic Groups.- 2. Systematic Enumeration of Cosets.- 3. Graphs, Maps and Cayley Diagrams.- 4. Abstract Crystallography.- 5. Hyperbolic Tessellations and Fundamental
Triangulated polygons and frieze patterns
First, a lesson in architecture. A frieze is a horizontal band of decoration around a building. These are some friezes from buildings in Ancient Persepolis. Note how they feature symmetrical,
Discrete Groups Generated by Reflections
1-3. Polytopes with restricted dihedral angles 590 4-7. Fundamental regions 594 8. The abstract definition 599 9. Complete enumeration of the irreducible groups 601 10-13. Continued products of the
Regular Complex Polytopes
Frontispiece Preface to the second edition Preface to the first edition 1. Regular polygons 2. Regular polyhedra 3. Polyhedral kaleidoscopes 4. Real four-space and the unitary plane 5. Frieze
A practical method for enumerating cosets of a finite abstract group
An important problem in finite-group theory is the determination of an abstract definition for a given group , that is, a set of relations between k generating operations S 1 , …., S k of , such that
REGULAR HONEYCOMBS IN HYPERBOLIC SPACE
made a study of honeycombs whose cells are equal regular polytopes in spaces of positive, zero, and negative curvature. The spherical and Euclidean honeycombs had already been described by Schlaf li
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