... theory.^4.1

C. O. Oakley and R. J. Wisner, FLEXAGONS. American Mathematical Monthly, Vol. LXIV, No 3, March 1957, Pp. 143-154.

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... later^4.2

Incoming and outgoing hinges of the pat will overlap, so that a complete pat is not formed, yet further winding is frustrated

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... flexagons ^6.1

However, Dr. F. G. Mannsell and Miss Joan Crampin (see bibliography) considered flaps, and presently (sect _____) we will study flexagons having superimposed hinges.

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... cycle ^6.2

A cycle is defined as a series of flexes from a given side back to that side without retracing any path or turning the flexagon over.

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... 0 ^6.3

From now on we will consider only the top unit when discussing which pat the flexagon peels from in flexing. Thus one hinged in the order 1 2 3 0 is called a left-flexing flexagon, while one hinged in the order 3 2 1 0 is a right-flexing flexagon

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... leaf ^6.4

An $n$-hinge is one which occupies position $n$ when a unit is folded together in such a way that the zero hinge connects the two units of the flexagon.

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... ^6.5

This tubulation, if cut and turned inside out, would produce a four-cycle. In general, if the effective hinge of a tubulation is $(G-r)$, the cycle attempted is $(r+1)$.

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... sides. ^7.1

Such a leaf is said to be of ``class G'', as is the corresponding flexagon.

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... ``cuts'' ^9.1

A ``cut'' is a shortcut flex which omits one or more sides. It is a classified by degree, representing the number of sides they cut out. A $0-$cut is a flex along the outside of the map polygon. In a proper flexagon, the $n-$cut is always an $(n+1)-$flex.

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... cycle ^9.2

A $0-$cut cycle ia one composed completely of $0-$cuts, no matter what the value of flexes involved. Thus, on the map it is equivalent to following along the outside edge of the map polygon.

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... flexing ^10.1

The notation ``$d-$face'' is used to indicate a face of degree $d$.

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... show ^10.2

``$(m,n)$'' refers to the face showing side $m$ on top and side $n$ below.

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.... ^10.3

$(A,B)^n$ is the face $(A,B)$ having face degree $n$.

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... Joseph^11.1

See bibliography

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... Wheeler ^12.1

See bibliography

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... followings: ^13.1

$f_n$ is the face degree and $D_n$ the sign sequence sum for the pat $n$; $D$ is the flexagon's total sign sequence sum.

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... 14.7) ^14.1

In fact, all regular flexagons are self-dual.

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