allTriangulations AallTriangulations(A, Homogenize => true, Fine => true, RegularOnly => true)This function constructs all triangulations of the point set corresponding to $A$ (or triangulation of the cone over $A$, if Homogenize => false is given. With no optional arguments, the default is to construct all regular triangulations.
This function is a wrapper for the topcom function topcomAllTriangulations, and has the same optional arguments as that function. This function returns a list of Triangulation (missing documentation) 's.
A triangulation is a list of list of the indices of the maximal simplices in the triangulation. (the index of the point corresponding to the $i$-th column (starting at $0$) is simply $i$.
For example, the following point set is the smallest which has a non-regular triangulation.
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The following code determines the support of each triangulation, and tallies them. Thus for example, we see that there are 6 regular fine triangulations.
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The method that topcom uses depends on the optional arguments Fine, ConnectedToRegular and RegularOnly.
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If the optional argument Fine is set to true, then only fine triangulations (i.e. those that involve every column of $A$) will be generated.
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If the optional argument RegularOnly is set to false, but ConnectedToRegular is true, it will generally take less time, as the program doesn't need to check each triangulation to see if it is regular.
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The following search would also yield all triangulations, even those not connected via bistellar flips to regular triangulations.
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Given the list of triangulations, we can query them using other topcom functions. See also Triangulations for other functionality.
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