Local modifications in planar hypohamiltonian graphs

We prove that for $n \geq 36$ there exists a planar hypohamiltonian graph of order $n$. As a corollary, we prove that for $n \geq 33$ there exists an almost hypohamiltonian planar graph of order $n$. Further, we exhibit over 100 planar hypohamiltonian graphs of order less than 40, including new grap