Are you ready to flip out? Hexaflexagons are six-sided, flat paper models that can be made to reveal hidden images through a series of flexes and folds. Flexagons were first introduced in a column written by Martin Gardner for Scientific American. From there, people started folding and figuring out creative ways to craft these interesting origami-like objects. Included in this delightful book are instructions and material to create hexaflexagons, tri-tetra flexagons, cubes, flexacubes, and more! Flexing kaleidocycles are shapes formed by taking several tetrahedra (four-sided 3D shapes) and joining their edges to form a ring, which can then be rotated so that it turns inside out to display a multitude different colors, shapes, and designs! This book contains: • A brief introduction on the history of hexaflexagons • Instructions on how to make 13 different fun flexagon models • 40 pages of easy tear-out pages with pieces to assemble your hexaflexagons People are still discovering new ways to innovate with these enjoyable creations—so with some study and practice, you may be able to come up with a unique design and enter the pages of flexagon history! All you need to do is to cut out and assemble the various models in this book to create the most intriguing and entertaining designs available. Start folding your flexagons now!

Japanese origami expert Hisao Fukui shows you how to create incredibly realistic paper birds and flying insects, a winged dinosaur and even an undulating Chinese dragon! The easy-to-follow folding instructions and photos in this book present 24 challenging and amazingly lifelike models--from intermediate to complex in terms of their level of difficulty. The 24 unique models in this book include: The Swan--The multilayered wings and body give this familiar model a major three-dimensional upgrade The Crane--Far from traditional, this crane rests on its built-in platform, and has an optional open wing configuration that can double as a fancy box Peacocks--One with tail feathers stowed neatly behind, and another with its tail fan proudly displayed The Swallow--Its distinctive bifurcated tail is on display in a kinetic diving pose The Crested Kingfisher--The artfully modeled eye of this hunter appears to be on the lookout for its next meal Stink Bug--there's nothing foul about this instantly recognizable shield-shaped insect model Beetles--A Horned Beetle with unfurled wings and a Rhinoceros Beetle with an intimidating spiky head Flying Chinese Dragon--Segmented and supple, this ancient symbol of power and good fortune is poised to pounce The Dragonfly--This incredibly detailed form is the most challenging model here, but the spectacular results are well worth the effort And many more!

Flexagons are hinged polygons that have the intriguing property of displaying different pairs of faces when they are flexed. Workable paper models of flexagons are easy to make and entertaining to manipulate. Flexagons have a surprisingly complex mathematical structure and just how a flexagon works is not obvious on casual examination of a paper model. Flexagons may be appreciated at three different levels. Firstly as toys or puzzles, secondly as a recreational mathematics topic and finally as the subject of serious mathematical study. This book is written for anyone interested in puzzles or recreational maths. No previous knowledge of flexagons is assumed, and the only pre-requisite is some knowledge of elementary geometry. An attractive feature of the book is a collection of nets, with assembly instructions, for a wide range of paper models of flexagons. These are printed full size and laid out so they can be photocopied.

The first of fifteen updated editions of the collected Mathematical Games of Martin Gardner, king of recreational mathematics.

A flexagon is a motion structure that has the appearance of a ring of hinged polygons. It can be flexed to display different pairs of faces, usually in cyclic order. Flexagons can be appreciated as toys or puzzles, as a recreational mathematics topic, and as the subject of serious mathematical study. Workable paper models of flexagons are easy to make and entertaining to manipulate. The mathematics of flexagons is complex, and how a flexagon works is not immediately obvious on examination of a paper model. Recent geometric analysis, included in the book, has improved theoretical understanding of flexagons, especially relationships between different types. This profusely illustrated book is arranged in a logical order appropriate for a textbook on the geometry of flexagons. It is written so that it can be enjoyed at both the recreational mathematics level, and at the serious mathematics level. The only prerequisite is some knowledge of elementary geometry, including properties of polygons. A feature of the book is a compendium of over 100 nets for making paper models of some of the more interesting flexagons, chosen to complement the text. These are accurately drawn and reproduced at half full size. Many of the nets have not previously been published. Instructions for assembling and manipulating the flexagons are included.

Flexagons are a form of Origami paper folding, where the fonished model involves flexing that reveals different faces.