@article{(Open Science Index):https://publications.waset.org/pdf/10009756,
	  title     = {Restrictedly-Regular Map Representation of n-Dimensional Abstract Polytopes},
	  author    = {Antonio Breda d’Azevedo},
	  country	= {},
	  institution	= {},
	  abstract     = {Regularity has often been present in the form of regular
polyhedra or tessellations; classical examples are the nine regular
polyhedra consisting of the five Platonic solids (regular convex
polyhedra) and the four Kleper-Poinsot polyhedra. These polytopes
can be seen as regular maps. Maps are cellular embeddings of
graphs (with possibly multiple edges, loops or dangling edges) on
compact connected (closed) surfaces with or without boundary. The
n-dimensional abstract polytopes, particularly the regular ones, have
gained popularity over recent years. The main focus of research
has been their symmetries and regularity. Planification of polyhedra
helps its spatial construction, yet it destroys its symmetries. To our
knowledge there is no “planification” for n-dimensional polytopes.
However we show that it is possible to make a “surfacification”
of the n-dimensional polytope, that is, it is possible to construct a
restrictedly-marked map representation of the abstract polytope on
some surface that describes its combinatorial structures as well as
all of its symmetries. We also show that there are infinitely many
ways to do this; yet there is one that is more natural that describes
reflections on the sides ((n−1)-faces) of n-simplices with reflections
on the sides of n-polygons. We illustrate this construction with the
4-tetrahedron (a regular 4-polytope with automorphism group of size
120) and the 4-cube (a regular 4-polytope with automorphism group
of size 384).},
	    journal   = {International Journal of Mathematical and Computational Sciences},
	  volume    = {12},
	  number    = {11},
	  year      = {2018},
	  pages     = {214 - 217},
	  ee        = {https://publications.waset.org/pdf/10009756},
	  url   	= {https://publications.waset.org/vol/143},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 143, 2018},
	}