# name
Many regular triangulations and many polytopes

# metadata.dc.description.abstract[].value
We show that for fixed $d>3$ and $n$ growing to infinity there are at least $(n !)^{d-2 \pm o(1)}$ different labeled combinatorial types of $d$-polytopes with $n$ vertices. This is about the square of the previous best lower bounds. As an intermediate step, we show that certain neighborly polytopes (such as particular realizations of cyclic polytopes) have at least $(n !)^{\lfloor(d-1) / 2\rfloor \pm o(1)}$ regular triangulations.

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Many regular triangulations and many polytopes