... 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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... later4.2
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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... Joseph11.1
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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