partial

type State struct {
	Dimension              int                      // The dimension of the ambient space.
	Lattice                *integervector.Parent    // The lattice ZZ^dimension.
	Vertices               []*integervector.Element // The vertices of the polytope, as a slice of integer vectors.
	Facets                 [][]int                  // The facets of the polytope, where facets[i] is the slice containing the indices of vertices in the i-th facet.
	Normals                []*integervector.Element // The outward pointing normals to the facets.
	NeighbouringFacets     []map[int]int            // NeighbouringFacets[fid] is a map recording the facets that are known to neighbour the facet F with index fid. neighbouringFacets[fid][vid] records the facet id of the facet adjacent to F along the ridge of F specified by the vertex with index vid.
	Basechanges            []matrix.Matrix          // Basechanges[fid] is the change of basis matrix that maps the vertices of the facet F to the standard basis elements.
	NeighbouringVertices   map[int]int              // This specifies the neighbouring vertices to the initial (standard) facet. FIX ME am not exactly sure how yet.
	NeighboursInHyperplane []*integer.Element       // FIX ME I think this specifies which hyperplanes the vertices adjacent to the standard facet are in.
	ResumeFromHeight       *integer.Element         // The height from which to resume the search for the next vertex. If this is nil, we resume at the maximum possible height.
	ResumeFrom             *integervector.Element   // The place to resume the search for the next vertex. If this is nil, we resume at the lower bound.
	HasClosed              bool                     // True if and only if we have successfully closed the vertices of this state to a smooth Fano polytope.
}