Add new partitions in the (old) Windows part of your disk. The first one (i=4) is a new system partition, the second one (i=5) a recovery partition. The new OS X partition starts at ~91 GB and has a size of ~26 GB - which shouldn't affect the old (hidden, "lost") OS X partition:
gpt add -b 180000000 -i 4 -s 50000000 -t 48465300-0000-11AA-AA11-00306543ECAC /dev/disk0 gpt add -b 230000000 -i 5 -s 1269536 -t 426F6F74-0000-11AA-AA11-00306543ECAC /dev/disk0
Now you have to format the new 26 GB partition:
diskutil list newfs_hfs -v "TempSystem" -J /dev/disk0s4 #use the proper partition found in diskutil list. It should have a size of ~26 GB newfs_hfs -v "Recovery HD" -J /dev/disk0s5 #use the proper partition found in diskutil list. It should have a size of ~650 MB diskutil mount /dev/disk0s4
Exit Terminal by entering
exit
and quit it.Open Restore OS X and install OS X to the partition TempSystem.
Configure the new system and enable internet access. Don't initialize any "unknown" volumes if asked.
Enable the root user
Log-out as admin and log-in as root
Download and install wxHexEditor
Where does the Recovery HD partition start?
That's probably the most difficult part because you have to find a string which is not very specific. Jump almost to the beginning of your new main partition (in your case to sector 179999900)
Then enter "HFSJ" like in the picture below, search for this string twoseveral times and make readable! hand-written notes of the different offsets. To restore your old OS X you have to boot to Internet Recovery Mode later and all on-screen findings in the current temporary OS X will be lost!
The reason to search for the string "HFSJ" is that all HFSJ+ volumes contain this string in the third sector of its partition. The magic string may also occur later andup to 40 times cluttered over ~10000 sectors! Sometimes it's really difficult to find the proper sector. A second indicator for the beginning of the Recovery HD is at least one block of 0xFF in the end!tenth sector (or block(MagicString)+7) of the partition.