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Frontispiece

Preface to the second edition

Preface to the first edition

Regular polygons / 1：

Regular polyhedra / 2：

Polyhedral kaleidoscopes / 3：

Real four-space and the unitary plane / 4：

Frieze patterns / 5：

The geometry of quaternions / 6：

The binary polyhedral groups / 7：

Unitary space / 8：

The unitary plane, using quaternions / 9：

The complete enumeration of finite reflection groups in the unitary plane / 10：

Regular complex polygons and Cayley diagrams / 11：

Regular complex polytopes defined and described / 12：

The regular complex polytopes and their symmetry groups / 13：

Tables

Reference

Index

Answers to exercises

Frontispiece

Preface to the second edition

Preface to the first edition