Polytope Theory
Face structure, f-vectors, and the upper bound theorem.
Polytope Theory. Face structure, f-vectors, and the upper bound theorem.
Foundations and canonical references
The standard treatments of polytope theory approach the subject from complementary angles. Ziegler, Lectures on Polytopes (1995) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Open methodological questions for polytope theory include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1995Lectures on Polytopesziegler-1995
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