The linked files may be anywhere in the file system, not just in a direct parent. This will report all files with three or more hard links in your home directory, grouped by inode. You may have spotted one example, but there may be others of interest:
find ~ -type f -links +2 -printf 'inode %i links %n name %p\n' | sort -n
I don't have any 3-ways, but this is my test for global two-way hard links.
$ find ~ -type f -links +1 -printf 'inode %i links %n name %p\n' | sort -n
find: ‘/home/paul/.gvfs’: Permission denied
find: ‘/home/paul/.cache/dconf’: Permission denied
inode 6173828 links 2 name /home/paul/Calhoun.post
inode 6173828 links 2 name /home/paul/SandBox/JpgTool/Calhoun.again
inode 6296398 links 2 name /home/paul/SandBox/fileGroup/fileGroup.V05
inode 6296398 links 2 name /home/paul/SandBox/fileGroup/myHardLink