Last edited May 12, 2003 by wtbaker@uiuc.edu

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# 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