The mathematics of surfaces is a fascinating subject - lying as it does at the heart of much architecture, art and maths, engineering and science. John Sharp's innovative use of sliceforms to explore the properties of surfaces is here produced in a systematic way, providing the reader the tools to build surfaces from paper to explore their mathematical properties. The extensive commentary explains the mathematics behind particular surfaces. Chapters on using computers to generate slices and sample templates complete the book. An invaluable exercise in practical geometry that will stimulate ideas for the student, professionals involved in modelling surfaces and the enthusiast. Contents include: Introduction and Basic Techniques; Contours and profiles; Properties and Types of Surfaces; Surfaces of Revolution; Ruled Surfaces; Surfaces from Equations: Algebraic surfaces; Polyhedra; Variations and explorations; Using the Computer; Templates and further resources.