Author: Peter R. Cromwell, University of Liverpool development of the theory surrounding polyhedra and rigorous treatment of the mathematics involved. Buy Polyhedra by Peter R. Cromwell (ISBN: ) from Amazon’s Book Store. Everyday low prices and free delivery on eligible orders. In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with . Cromwell gives a similar definition but without the restriction of three edges per vertex. Again, this type of definition does not encompass the.

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Read, highlight, and take notes, across web, tablet, and phone. Account Options Sign in. In modern times, polyhedra and their symmetries have been cast in a new light by combinatorics an d group theory. This book comprehensively documents the many and varied ways that polyhedra have come to the fore throughout My library Help Advanced Polyhevra Search.

Cambridge University Press Amazon. Cambridge University PressJul 22, – Mathematics – pages. Polyhedra have cropped up in many different guises throughout recorded history.

This book comprehensively documents the many and varied ways that polyhedra have come to the fore throughout the development of mathematics.

The author strikes a balance between covering the historical development of the theory surrounding polyhedra, and presenting a rigorous treatment of the mathematics involved. It is attractively illustrated with dozens of diagrams to illustrate ideas that crowell otherwise prove difficult to grasp. Historians of mathematics, as well as those more interested in the mathematics itself, will find this unique book fascinating. Selected pages Title Page.


Contents Indivisible Inexpressible cro,well Unavoidable. A common origin for oriental mathematics. Crmwell mathematics and the discovery of incommensurability. The nature of space. What is a polyhedron? Equality Rigidity and Flexibility.

Liu Hui on the volume of a pyramid. Eudoxus method of exhaustion. Primitive objects and unproved theorems. The problem of existence. Constructing the Platonic solids. The discovery of the regular polyhedra. Polyhedra with regular faces.


Decline and Rebirth of Polyhedral Geometry. The decline of geometry. The rise of Islam. Collecting and spreading the classics. The restoration of the Elements. A new way of seeing. Fantasy Harmony and Uniformity.

The structure of the universe. Star polygons and star polyhedra.

Surfaces Solids and Spheres. Plane angles solid angles and their measurement. The announcement of Eulers formula. The naming of parts.

Consequences of Eulers formula. Exceptions which prove the rule.

Rotating rings and flexible frameworks. Are all polyhedra rigid? When are polyhedra equal? Stars Stellations and Skeletons. Cauchys enumeration of star polyhedra. Stellations of the icosahedron. Bertrands enumeration of star polyhedra.

Symmetry Shape and Structure.

Polyhedra by Peter R. Cromwell

Systems of rotational symmetry. How many systems of rotational symmetry are there? Compound symmetry and the S2n symmetry type. Determining the correct symmetry type. Crystallography and the development of symmetry. Counting Colouring and Computing. Colouring the Platonic solids. How many colourings are there? Applications of the counting theorem. How many colours are necessary? cro,well


Combination Transformation and Decoration. Are there any regular compounds? The space of cromwfll convex polyhedra. The solution of fifth degree equations. Other editions – View all Polyhedra Peter R.

Cromwell No preview available – Common terms and phrases angle sum antiprism Archimedean solids axes axis base Cauchy centre Chapter congruent constructed contains convex polyhedron crystals cub-octahedron cube definition deltahedron described dihedral angles dissection edges Elements equal equations equilateral Euclid Euler’s formula example face-planes face-transitive flexible polyhedron four geometry Greek H.

Coxeter hexagonal icosahedral icosahedron inscribed interior angles Kepler kernel kind labelled lemma mathematicians mathematics poljhedra plane number of colourings number of faces number of sides number of vertices objects octahedron Pacioli pattern pentagon pentagram perspective plane angles Platonic solids Poinsot prism problem produce proof rcomwell coloured properties pyramid regular polygons regular polyhedra regular solids result rhomb-cub-octahedron rhombic right angles rotational symmetry shown in Figure solid angle space sphere spherical polygon square star polygons star polyhedra structure surface symmetry group polyhdera operation symmetry type tetrahedron theorem triangles triangular faces truncated uncoloured vertex figures vertex-transitive volume yang-ma.

References to this book Geometry of Quantum States: Indivisible Inexpressible and Unavoidable. Geometry of Quantum States: