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\title{Euler's Polyhedron Formula}
\author{Lawrence C. Paulson}
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\begin{abstract}
Euler stated in 1752 that every convex polyhedron satisfied the formula $V - E + F = 2$ 
where $V$, $E$ and $F$ are the numbers of its vertices, edges, and faces. For three dimensions,
the well-known proof involves removing one face and then flattening the remainder to form a planar graph,
which then is iteratively transformed to leave a single triangle. The history of that proof is extensively
discussed and elaborated by Imre Lakatos~\cite{lakatos}, leaving one finally wondering whether
the theorem even holds. The formal proof provided here has been ported from HOL Light, 
where it is credited to Lawrence~\cite{lawrence-short}. The proof generalises Euler's observation
from solid polyhedra to convex polytopes of arbitrary dimension.
\end{abstract}

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\paragraph*{Acknowledgements}
The author was supported by the ERC Advanced Grant ALEXANDRIA (Project 742178) funded by the European Research Council. 

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