Since this information seems to be available only on the badge pages, I threw together a quick userscript (direct install link) to add the filter options.
Warning: browsing through the 630 pages of the Reviewer badge on Stack Overflow took half an hour. Use with caution!
... when looking at the Summary of Accounts in a user's profile, the badges for all sites use the icon for the site that the viewer is viewing the page from at that time.
There aren't individual files for each site's favicon, they are all in one file. Some sites use one style of badge for all three and some have three different styles.
The favicon for each ...
Using this query, its possible to see the number of days that count towards the next badge, and in theory when you have 200 of them, you will get your next Socratic badge.
However, since deleted questions aren't in the query the number of days is overestimated. I had 207 positive days when I got my second Socratic badge. Also if your positive question ...