Dyh-Tau (17073 ft). Main Summit through Right S. Buttress.

Starting from the campground at Djangi-kosh go up the left moraine of the Bezymyannyi (Nameless) glacier for about 1000 feet. Then diverge to the right and climb talus and snow slope up to the glacier under the SE spurs of Bezymyannaya (Nameless) Mountain (13287ft).
From the glacier up and right through the snow couloir or easy rock (3'th-4'th grade) climb up to the snow-firn plateau under the S wall of Dyh-tau massif. There is an ice-snow couloir coming down from the base of the white wall with bright red-yellow stripe (the wall is in the upper part of the SW ridge of the Dyh-tau). Climb 3'th - 5'th grade rock of the left side of the couloir, then traverse to the right side (caution: rock falls!). There is a place for bivy under the white wall, so called "Chernye Osypi" (Black gravel or Black talus). Approximate time from the campground is about 7-8hous. To avoid rockfalls, it is highly recommended to set off from the campground as early as 5 or 6 am.
From the bivy cross a snow plateau up to the left and climb snow-rock couloir to the wide gravel ledge, crossing the whole S wall of the Dyh-tau massif.
On the ledge go to the right, cross two 140 ft. snow-ice couloir and down climb 12 ft. wall (loose blocks!) to the narrow snow couloir (caution: rock fall!). Climb the couloir up and to the right to the easy rocks of the Right Buttress.
Climb 500 feet of the easy rocks up the Right Buttress to the shoulder under ~250 feet rock band. To cross this rock band climb 120 feet cleft to the right of the icy vertical gutter. Then climb steep 100 feet snow-ice couloir, and exit from this couloir up-right through 60 feet slab to the ledge. After you crossed the rock band, you'll see a cairn on the ledge after slab.
From this ledge climb up approx. 600 feet of the polished slab. There is 25 feet wall in the center of the slab, climb the corner in this wall and exit to the right onto a low profile ridge. From the slab climb the right-facing wall and corners about 250 feet up and right to another easy slab. Climb approx. 270 feet and move to the left into the snow-ice couloir. Climb its left slope up to the second rock band.
Exit couloir to the right side of the wall and climb in 40 feet up to a ledge. Traverse the ledge and moderate rock 250 feet to the right, and starting from the feather-like flake climb a wall up and right for about 120 feet. Continue up snow ridge and slope for about 300 feet to the junction of right and central S buttresses. You can find a bivy spot on a snow ridge above the third gendarme. From bivy on the Black Gravel it usually takes 12 hours to get here.
From the bivy move up 150-feet rock-snow ridge itself, or its right side, to a rock rise. Climb the right side of the rise, stepping into the snow couloir from time to time, or move up through the couloir itself to the top of the rise (With some ingenuity, you can make a good bivy spot here).
After the rise move 180 ft to the right, passing snow couloir and rock slope to a ridge. Climb sharp but crushed ridge up-left 240 feet to the base of the fourth gendarme. Climb 60 feet wall and sharp 40 feet ridge to the top of gendarme. Alternatively, you can climb to the top of the fourth gendarme straight from the snow ridge atop of the rock rise (300-350 feet snow-covered rocks). Rappel 25 feet slab and ridge from gendarme to a mould at the base of the fifth gendarme "Zub" ("Tooth").
Circumvent the "Tooth" from the left side, traversing 120 feet at the boundary of the rock and ice, then climb up 600-700 feet of the easy rock and snow ridge to the base of the sixth gendarme.
Escape sixth gendarme traversing to the left 120 feet, then climbing 150 feet of slabs to the ridge behind the gendarme. Then climb 1000 feet of easy and moderate rocks of the ridge up to the base of the summit tower. There are two way to climb the summit tower.
1) Climb straight up through a 30 feet chimney, then traverse through a wide sloppy ledge 25 feet to the right and then climb 100 feet chimney to an overhanging choke-stone. Escape the choke-stone to the right and then climb 150 feet of easy snow-covered rock to the summit.
2) At the base of the tower traverse 120 feet to the left, then climb 50 feet ice-snow couloir , then continue for another 240 feet on the left side of the couloir to the N ridge. Then diverge to the right and climb easy ridge and 12 feet cleft to the summit.
Starting from the bivy above the third gendarme it takes 12-15 hours to summit.
To descent rappel down to the junction between two summits of Dyh-tau, then continue down Central S Couloir (total 21 - 23 rappels to the gravel ledge crossing the S wall, slings are set approximately each 120 feet). Alternatively you descend through the North Ridge.
Suggestions.
1. Team size 4-5 people.
2. Starting bivy - Black gravel bivy, starting time 4-5 am.
3. Alternative bivies: near the cairn, on the slab below the first rock band, atop of the rock rise under the fourth gendarme, under the fifth gendarme "Tooth", on the ridge under the summit tower.
Afterword:
Here I translated description as it appears in the official guidebook of the Bezengi camp. However, there are countless variations and almost every party find their own way in this labyrinth. Diverging from this description does not diminish the difficulty, most likely it is the other way round. Leader can climb in mountaineering boots and with light backpack, average difficulty of the route is about 5.4 - 5.5. Nevertheless, climbing shoes are very welcomed for several crux pitches, which might be up to 5.7+. In less favorable conditions, you'll have to negotiate those pitches with your crampons on.

Regular rock gear, couple of screws in case you missed rap. slings