Download website icons with Favicon Downloader. Favicon Downloader can download all the different icons a website provides for various platforms including:

-apple-touch-icon
-apple-touch-icon-precomposed
-shortcut icon
-mask-icon (mask-icon is an SVG image websites can provide for Safari tabs).
-Web app icons used in Android.
-Microsoft Pinned Site icons.
-Google TV icons.

You can type a website address in the app to view all the icons the website provides and optionally save the image files on your Mac.