typedef struct Vertex {
  unsigned id;
  double*  point;
} VertexT;

typedef struct FullVertex {
  unsigned  id;
  double*   point;
  unsigned* neighfacets;
  unsigned  nneighfacets;
  unsigned* neighvertices;
  unsigned  nneighsvertices;
  unsigned* neighridges;
  unsigned  nneighridges;
} FullVertexT;

typedef struct SetOfVertices {
    VertexT*   vertices;
    unsigned   nvertices;
} SetOfVerticesT;

typedef struct Ridge {
    VertexT*   vertices;
    unsigned   ridgeOf1;
    unsigned   ridgeOf2;
    unsigned   nvertices;
    unsigned   id;
    unsigned** edges;
    unsigned   nedges;
} RidgeT;

typedef struct Face {
  VertexT*   vertices;
  unsigned   nvertices;
  RidgeT*    ridges;
  unsigned*  ridgesids;
  unsigned   nridges;
  double*    center;
  double*    normal;
  double     offset;
  int        orientation;
  double     area;
  unsigned*  neighbors;
  unsigned   neighborsize;
  int        family;
  unsigned** edges;
  unsigned   nedges;
} FaceT;

typedef struct ConvexHull {
  unsigned     dim;
  FullVertexT* vertices;
  unsigned     nvertices;
  FaceT*       faces;
  unsigned     nfaces;
  RidgeT*      ridges;
  unsigned     nridges;
  unsigned**   edges;
  unsigned     nedges;
  unsigned     triangle;
} ConvexHullT;