Flag Numbers and FLAGTOOL

FLAGTOOL is a computer program for proving automatically theorems about the combinatorial structure of polytopes of dimensions at most 10. Its starting point is the known linear relations (equalities and inequalities) for flag number of polytopes. After describing the state of the art concerning such linear relations we describe various applications of FLAGTOOL and we conclude by indicating several directions for future research and automation. As an appendix we describe FLAGTOOL’s main tools and demonstrate one working session with the program.

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