ADDITIONAL FILES C4P_Boy_C3B_with_dual_Boy_surface.hexas the regular cubical 3-ball with a dual Boy's surface; stored in HEXAS file format (see below). template_XXXXX_cubification.hexas template_XXXXX_vertexstar.gif The set of templates used to produced the file above. For each type of a vertex star of a normal crossing grid immersion of a 2-dimensional manifold there the set of templates includes a regular cubial subdivision of a standard cube. c4p.rules A polymake rules file. To be used for the verification of the polytope instance (without calculating the HASSE_DIAGRAM). HEXAS FILE FORMAT This is a non-standard polymake file format for storing regular hexa complexes. It used two non-standard sections, namely LIFTED_COMPLEX_POINTS and HEXAS. The first section describes the ``lifted´´ points of the complex as homogenous coordinates, where the last coordinate gives a height function. Each line of the HEXAS section describes a facet of this 3-dimensional cubical complex as follows: Each line is a vector v_1, v_2, ..., v_8 of complex point indices (0 is the first index) of length eight; v_1,...,v_4 are the indices of the base quadrangle in cyclic order, and v_5, ..., v_8 form the top facet. (v_1 is adjacent to v_2, v_4 and v_8).