eBook - PDF

Origami Polyhedra Design

Name: Origami Polyhedra Design
ISBN: 9781439871065

John Montroll,

302 pages
English
PDF
Available on iOS & Android

eBook - PDF

Origami Polyhedra Design

John Montroll,

About this book

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,

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Yes, you can access Origami Polyhedra Design by John Montroll in PDF and/or ePUB format, as well as other popular books in Mathematics & Games in Mathematics. We have over one million books available in our catalogue for you to explore.

Information

Publisher

Year

Print ISBN

eBook ISBN

Topic

Subtopic

Index

Designing 

Origami

Polyhedra

Part

I

3

Polyhedra 

Overview

Polyhedra 

are

three-dimensional 

shapes 

composed 

of

polygons, 

two-dimensional 

shapes 

composed 

of

straight 

lines. 

Here 

we

present 

some 

of

the

names 

associated 

with 

polyhedra.

Concave 

Polyhedra

If

there 

are

any

lines 

connecting 

two

points 

on

the

surface 

that 

are

outside 

the

polyhedron 

(as

in

the

first

picture 

below), 

even 

partially, 

then 

the

polyhedron 

is

concave, 

or

nonconvex.

Sunken 

Cube

(Sunk)

Platonic 

Solids

A

Platonic 

solid 

is

a

convex 

polyhedron 

composed 

of

identical 

regular 

polygons 

with 

identical 

vertices. 

Thus,

all

of

the

edges 

are

the

same 

length, 

the

same 

number 

of

edges 

meet 

at

each 

vertex, 

and

all

the

faces 

are

the

same 

shape. 

There 

are

five 

Platonic 

solids: 

the

tetrahedron, 

cube, 

octahedron, 

icosahedron, 

and

dodecahedron.

Tetrahedron

Cubehemioctahedron

(Dimpled)

Stellated 

Cube

(Star)

Convex 

Polyhedra

Take 

any

two

points 

on

the

surface 

of

a

polyhedron 

and

picture 

a

line 

connecting 

them 

(as

in

the

first 

picture

below). 

A

polyhedron 

is

convex 

if

all

such 

lines 

are

either 

on

the

surface 

of

the

polyhedron 

or

are

completely

inside 

the

polyhedron.

Icosahedron

Cube

Octahedron

Icosahedron

Dodecahedron

Hexagonal

Dipyramid

Pentagonal

Pyramid

Front Cover
Table of Contents
Symbols
Basic Folds
Introduction
Part I
Part II
Part III
Back Cover

About this book

Frequently asked questions

Information

Table of contents