Creating new symbol derived from hash

Creating new symbol derived from hash

I rotating the hash (#) about 45 degrees by command:
\newcommand{\hash}{\mathbin{\rotatebox[origin=c]{45}{$\#$}}}
I used it:
\[
\B(\R^n) = \B(\R^r) \hash_{\sigma} \B(\R^s) \text{, gdzie }
\]
\[
\B(\R^r) \hash_{\sigma} \B(\R^s) = \sigma(\{ A \times B : A \in
\B(\R^r), B \in \B(\R^s) \})
\]
and it look like:

but it don't look beauty. I would like to ask how make it (symbol inside
red polygon) in more elegant way.