  A polyhedral map is called $\{p, q\}$-equivelar if each face has $p$ edges
and each vertex belongs to $q$ faces. In 1983, it was shown that there exist
infinitely many geometrically realizable $\{p, q\}$-equivelar polyhedral maps
if $q > p = 4$, $p > q = 4$ or $q - 3 > p = 3$. It was shown in 2001 that there
exist infinitely many $\{4, 4\}$- and $\{3, 6\}$-equivelar polyhedral maps. In
1990, it was shown that $\{5, 5\}$- and $\{6, 6\}$-equivelar polyhedral maps
exist. In this note, examples are constructed, to show that infinitely many
self dual $\{k, k\}$-equivelar polyhedral maps exist for each $k \geq 5$. Also
vertex-minimal non-singular $\{p, p\}$-pattern are constructed for all odd
primes $p$.
