Abstract

Semi Regular Lattice Polyhedra

Highlights

  • In 1985 two mathematicians, Peter Hilton and Jean Pederson have done a research on the folding regular star polygons

  • They have taken benefit from a practical method which is, folding paper, for proving the number of existence of regular polygons (Hilton & Pederson, 1985), and the way they have used is similar to the way which we used

  • In 1988, Bokowski and Wills described some fundamental ideas in the study of regular maps and their polyhedral realizations in the Euclidean 3-space (Bokowski & Wills, 1988)

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Summary

Introduction

In 1985 two mathematicians, Peter Hilton and Jean Pederson have done a research on the folding regular star polygons They have taken benefit from a practical method which is, folding paper, for proving the number of existence of regular polygons (Hilton & Pederson, 1985), and the way they have used is similar to the way which we used. X, y and z are all integers, and so a polygon in R3 is called lattice polygon if all its vertices are lattice point. (Diested,2005; Scott, 1987) A polyhedra is a solid which comes to existence by union of some intersecting planes in which any two planes cut each other, and it is regular if its faces are congruent regular polygons; and each vertex has the same number of faces surrounding it. A semiregular polyhedra has regular polygons as faces and all vertices congruent, but they admit a variety of such polygons in one solid. A polyhedra in R3 is called lattice if all its vertices are lattice points

Some information about the main subject
Regular and Semi Regular Lattice Polyhedra
Now we want to prove that there are thirteen semiregular polyhedra

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