... 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 -hinge is one which occupies position 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 , the cycle attempted is .
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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 cut is a flex along the outside of the map polygon. In a proper flexagon, the cut is always an flex.
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... cycle 9.2
A cut cycle ia one composed completely of 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 ``face'' is used to indicate a face of degree .
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... show 10.2
``'' refers to the face showing side on top and side below.
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.... 10.3
is the face having face degree .
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... Joseph11.1
See bibliography
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... Wheeler 12.1
See bibliography
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... followings: 13.1
is the face degree and the sign sequence sum for the pat ; 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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