  In this article we present a pheno-inspired classification for the divisor
topologies of the favorable Calabi Yau (CY) threefolds with $1 \leq h^{1,1}(CY)
\leq 5$ arising from the four-dimensional reflexive polytopes of the
Kreuzer-Skarke database. Based on some empirical observations we conjecture
that the topologies of the so-called coordinate divisors can be classified into
two categories: (i). $\chi_{_h}(D) \geq 1$ with Hodge numbers given by
$\{h^{0,0} = 1, \, h^{1,0} = 0, \, h^{2,0} = \chi_{_h}(D) -1, \, h^{1,1} =
\chi(D) - 2 \chi_{_h}(D) \}$ and (ii). $\chi_{_h}(D) \leq 1$ with Hodge numbers
given by $\{h^{0,0} = 1, \, h^{1,0} = 1 - \chi_{_h}(D), \, h^{2,0} = 0, \,
h^{1,1} = \chi(D) + 2 - 4 \chi_{_h}(D)\}$, where $\chi_{_h}(D)$ denotes the
Arithmetic genus while $\chi(D)$ denotes the Euler characteristic of the
divisor $D$. We present the Hodge numbers of around 140000 coordinate divisors
corresponding to all the CY threefolds with $1 \leq h^{1,1}(CY) \leq 5$ which
corresponds to a total of nearly 16000 distinct CY geometries. Subsequently we
argue that our conjecture can help in ``bypassing" the need of cohomCalg for
computing Hodge numbers of coordinate divisors, and hence can be significantly
useful for studying the divisor topologies of CY threefolds with higher
$h^{1,1}$ for which cohomCalg gets too slow and sometimes even breaks as well.
We also demonstrate how these scanning results can be directly used for
phenomenological model building, e.g. in estimating the $D3$-brane tadpole
charge (under reflection involutions) which is a central ingredient for
constructing explicit global models due to several different reasons/interests
such as the de-Sitter uplifting through anti-$D3$ brane and (flat) flux vacua
searches.
