Visio 2013 files (vsdx) dont show the Visio Icon when I use the SharePoint search. Is there an easy fix for that? Adding a result type doesn't work.
You could copy the out of the box Word or PowerPoint display template and improve it. There is a result type rule for "Visio" but it appears to ignore VSDX files. You could even go so far as to produce a hover panel using Visio Services to display a preview of the file! If all you want it the proper icon. I would copy the Office Document display template (Item_OfficeDocument.html) and use the icvsdx.gif icon.