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E-grāmata: Origami Polyhedra Design

4.85/5 (26 ratings by Goodreads)
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This book unravels the mystery of Geometry in Origami with a unique approach: 64 Polyhedra designs, each made from a single square sheet of paper, no cuts, no glue; each polyhedron the largest possible from the starting size of square and each having an ingenious locking mechanism to hold its shape.The author covers the five Platonic solids (cube, tetrahedron, octahedron, icosahedron and dodecahedron). There are ample variations with different color patterns and sunken sides. Dipyramids and Dimpled Dipyramids, unexplored before this in Origami, are also covered. There are a total of 64 models in the book. All the designs have an interesting look and a pleasing folding sequence and are based on unique mathematical equations.

American origami master Montroll, the genius behind the single-square, no cuts, no glue approach; has created many famous designs and written several books. Here he focuses on folding single sheets into three-dimensional shapes to augment the recent interest in multi-sheet polyhedra. He covers designing origami polyhedra, platonic and related polyhedra, and dipyramids and dimpled dipyramids. His diagrams conform to international notation, and the difficulty of each figure is marked as one of four levels from simple to very complex. Annotation ©2010 Book News, Inc., Portland, OR (booknews.com)

Recenzijas

... a teacher of geometry because it allows students to fold figures ranging from simple two-dimensional polygons to complex three-dimensional figures ... can easily be blended into the regular classroom curriculum ... an excellent resource. I recommend it for geometry teachers as a supplement to their regular curriculum. Gary S. Luck, University of Wisconsin-Milwaukee, Milwaukee, USA

It covers a truly wide range of objects, including the Platonic polyhedra, di-pyramids and some stellated or sunken counterparts. The staggering thing is that each and every example is made of one single sheet of paper. It is astonishing what is possible in the realm of origami. The procedures of generating such a model are explained step by step, which enables the reader to follow the recipe. I sincerely recommend this nice and absorbing book for all afficionados of origami. O. Roschel, International Mathematical News (IMN), December 2010

Origami's recent explosive increase in sophistication owes much to the pioneering ingenuity of noted origami artist Montroll, as documented by his more than two dozen books published since 1980. ... The present volume collects instructions for folding diverse polyhedra, both convex and concave, including many beautiful variations on Platonic solids, more than 70 models in all. ... Notwithstanding the considerable detail the author provides regarding the matematical proportions, miraculously, the folding processes generally involve no explicit numerical measurement. ... Highly recommended. D. V. Feldman, CHOICE, August 2010

Origami Polyhedra Design is a breakthrough collection of original designs created by the author to make polyhedral shapes from a single sheet of paper through folding. In modular origami, a polyhedral shape is built by interlocking many identical origami pieces, where each piece is constructed from a separate sheet of paper. In this book, Montroll, an origami master who pioneered the folding of origami animals from a single sheet of paper, presents methods for folding various polyhedra from a single sheet of paper. The book is well designed and organized and makes you want to start folding polyhedra. ... and the instructions for the individual models are clear and easy to understand... Thomas Hagedorn, MAA Reviews, April 2010

Symbols xi
Basic Folds xii
Introduction xiii
Designing Origami Polyhedra
1(60)
Polyhedra Overview
3(4)
Design Factors and Techniques
7(12)
Math and Design
19(20)
Design Method Examples
39(6)
Polygons
45(16)
Equilateral Triangle
46(2)
Pentagon
48(4)
Hexagon
52(2)
Heptagon
54(2)
Octagon
56(1)
Silver Rectangle
57(1)
Bronze Rectangle
58(1)
Golden Rectangle
59(2)
Platonic and Related Polyhedra
61(110)
Tetrahedron Design
63(20)
Tetrahedron
65(2)
Duo-Colored Tetrahedron
67(2)
Striped Tetrahedron
69(3)
Tetrahedron of Triangles
72(4)
Stellated Tetrahedron
76(3)
Dimpled Truncated Tetrahedron
79(4)
Cube Design
83(30)
Cube
87(2)
Striped Cube
89(3)
Triangles on Cube
92(3)
Cube with Squares
95(3)
Stellated Octahedron
98(2)
Cubehemioctahedron
100(4)
Dimpled Rhombicuboctahedron
104(4)
Stacked Cubes
108(5)
Octahedron Design
113(22)
Octahedron
115(3)
Striped Octahedron
118(3)
Duo-Colored Octahedron
121(3)
Stellated Cube
124(3)
Octahemioctahedron
127(4)
Dimpled Truncated Octahedron
131(4)
More Platonic Solids Design
135(12)
Icosahedron
137(3)
Dodecahedron
140(7)
Sunken Platonic Solids Design
147(24)
Sunken Octahedron
150(3)
Sunken Tetrahedron
153(4)
Sunken Cube
157(4)
Sunken Dodecahedron
161(5)
Sunken Icosahedron
166(5)
Dipyramids and Dimpled Dipyramids
171(117)
Dipyramid Design
173(70)
Triangular Dipyramid 90°
178(2)
Triangular Dipyramid
180(3)
Triangular Dipyramid in a Sphere
183(3)
Tall Triangular Dipyramid
186(3)
Tall Square Dipyramid
189(3)
Silver Square Dipyramid
192(2)
Squat Silver Square Diamond
194(3)
Pentagonal Dipyramid
197(4)
Pentagonal Dipyramid 45°
201(2)
Pentagonal Dipyramid in a Sphere
203(3)
Golden Pentagonal Dipyramid
206(2)
Squat Golden Pentagonal Dipyramid
208(2)
Hexagonal Dipyramid
210(3)
Silver Hexagonal Dipyramid
213(1)
Hexagonal Dipyramid 36°
214(1)
Hexagonal Dipyramid in a Sphere
215(3)
Squat Silver Hexagonal Dipyramid
218(1)
Heptagonal Dipyramid
219(4)
Heptagonal Dipyramid 30°
223(2)
Heptagonal Dipyramid in a Sphere
225(4)
Octagonal Dipyramid
229(3)
Octagonal Dipyramid 26°
232(2)
Octagonal Dipyramid in a Sphere
234(3)
Nonagonal Dipyramid
237(3)
Decagonal Dipyramid
240(3)
Dimpled Dipyramid Design
243(45)
Tall Dimpled Square Dipyramid
247(3)
Dimpled Silver Sqare Dipyramid
250(4)
Heptahedron
254(4)
Dimpled Squat Square Dipyramid
258(4)
Tall Dimpled Hexagonal Dipyramid
262(5)
Dimpled Silver Hexagonal Dipyramid
267(3)
Dimpled Hexagonal Dypyramid
270(5)
Dimpled Hexagonal Dipyramid in a Sphere
275(5)
Octagonal Flying Saucer
280(3)
Dimpled Octagonal Dipyramid in a Sphere
283(4)
Dimpled Octagonal Dipyramid
287(1)
Dimpled Silver Octagonal Dipyramid
288
John Montroll, St. Anselm's Abbey School, Washington, D.C., USA