Last edited May 12, 2003 by wtbaker@uiuc.edu
Find this document at http://www.ncsa.uiuc.edu/Classes/MATH198/wtbaker/project.html
Back Home



illiHedron:

The Permutahedron and Associahedron


Abstract:

This project is centered on the permutahedron and associahedron. The permutahedron and associahedron are geometric shapes that represent several concepts of combinatorial mathematics, the details of which can be found in the research section below. Specifically for this project, the permutahedron for n=4 and the associahedron for n=5 (five factors) have been created, and there has been an emphasis on designing ways to represent their combinatorial properties visually (i.e. how do we represent the information that is represented by each of the vertices of these two polyhedrons without the use of text, or other text based guides). These two objects correspond to polyhedrons that contain 24 and 14 vertices respectively. Using illiSkel and CAVEskel as a guide, both of these objects can be created and can be viewed on either a regular monitor, or in the CAVE. However, the code attached is the version that does not run in the CAVE (the CAVE code was made by moving the attached code into CAVEskel, but the ways in which the objects are drawn is the same in both versions).

Permutahedron and Associahedron Operating Instructions

Permutation and Associahedron Code Explanation

Research/Mathematics of the Permutahedron and Associahedron

References

illiHedron Photos