# Infinity-fin

The $\infty$-fin is a continuum comprised of an infinite sequence of $2$-cells $a_1,a_2,\ldots$ with the property that given any $i$ and $j$, $a_i \cap a_j=\{v\}$ for some point $v$ called the vertex, and $\displaystyle\lim_{k \rightarrow \infty} \mathrm{diam}(a_k)=0$.