This section lists functions for the construction of some special families of origamis.
‣ RandomOrigami( d ) | ( function ) |
Returns: An Origami
This function returns a random origami of degree \(d\). It is usually used for testing. As it is randomised over its permutations, the probability distribution is not guaranteed to be uniform on the orbits.
‣ XOrigami( n ) | ( function ) |
Returns: A special origami
This function returns special origamis, so called Xorigamis. Xorigamis have degree \(2n\). The horizontal permutation is the \(2n\)-cycle \((1,\ldots, 2n)\) and the vertical permutation is of the form:
\[(1,2)(3,4)..(2n-1,2n)\]
gap> XOrigami(2); Origami((1,2,3,4), (1,2)(3,4), 4)
‣ ElevatorOrigami( a, b, d ) | ( function ) |
Returns: A special origami
The elevator origami consists of \(d\) steps of height \(b\) and length \(a\). The last step is connected to the first step.
gap> Elevator(2,0,3); Origami((1,2)(3,5)(4,6), (1,3)(2,4)(5,6), 6)
‣ StaircaseOrigami( a, b, d ) | ( function ) |
Returns: A special origami
The staircase origami consists of \(d\) steps of height \(b\) and length \(a\).
gap> Staircase(2,0,3); Origami((1,2)(3,4)(5,6), (2,3)(4,5), 6)
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