from application fan
This represents a stacky fan built from the orbit of a fan F under a group G that permutes the homogeneous coordinates of F's rays. It is assumed, but currently not checked, that the interior of F does not intersect the interiors of its images.
Scalar: numeric data type used for the coordinates, must be an ordered field. Default is Rational.
These properties capture information of the object that is concerned with the action of permutation groups.
GENERATING_HASSE_DIAGRAMThe HASSE_DIAGRAM of the fan that was used to generate it. Must be of type Sequential because Cone::HASSE_DIAGRAM has that type
GENERATING_MAXIMAL_CONESThe MAXIMAL_CONES of the fan that were used to generate it.
GENERATING_RAYSThe RAYS of the stacky fan that were used to generate it.
Matrix<Scalar,NonSymmetric>
N_GENERATING_RAYSThe number of RAYS of the stacky fan that were used to generate it. By the way orbit_fan works, these rays also show up at the beginning of the RAYS matrix.
ORIGINAL_RAYS_ACTION_GENERATORSfor higher barycentric subdivisions, store the original RAYS_ACTION.GENERATORS They are stored outside of a GROUP object, because these generators act on the elements of the innermost sets of the VERTEX_LABELS, but not on anything directly in the object itself
STACKY_FACESFrom a fan F equipped with a symmetry group G acting on the coordinates, * such that the interior of F does not intersect the interiors of its images,* calculate the faces of F of all dimensions that lie in distinct orbits of G.F The data is organized as an array, one entry for each dimension starting with 1; each entry is a Set, one for each orbit of that dimension; each entry is a Set<Set<Int» of faces Set<Int> in that orbit that lie in F
STACKY_F_VECTORCounts the number of STACKY_FACES
VERTEX_LABELSVertex labels as an array of Set<Set<Int». This is more efficient than the String type used in topaz::SimplicialComplex