Approach from Camp Bezengi.
Leave over the grassy fields in direction of Mizhirgi Glacier. Always stay on the right side of it. The trail is easy to follow the whole first day (un-acclimatized) until you hit the first snowfields. There are some very good camp spots every hour or so. Meadows with fresh water nearby. When hitting the snowfields you have to be alert to follow the track as it's disappearing under rock-slide zones, old avalanches etc.
Be alert for falling rocks. Better stay a bit out on the snowfields at some places.
All of a sudden the dizzying views of Dychtau's 2000m high north face shows up and you're almost at the same time hitting grassy slopes again. This is where most Dychtau climbers set camp and it's an excellent place to stash gear or food for later. Take right here and follow the sometimes very steep paths (45 degr.) up the hill until you're at a little plataeu with old camp-platforms. It's a high risk these are covered with snow. The next part of the route is demanding and if tired here - stop for the night. Safe camping and strategically in the right spot for the next day.
A glacier wall is in front of you. A rock face constantly producing rocks on your right. Be very careful walking past this area when warm or sunny. When you have passed the glacier on the right hand side, a steep slope has to be negotiated. 40-50 degrees on snow and ice. Some crevasses on you right, but they're quite small.
When this sometimes tricky part has been climbed, you're at a huge snowfield which covers the Kursantov Glacier. Keep on the right hand side and put camp before it gets too steep. Misses Tau is now looming over you.
Some walking in (probably deep) snow takes you to the North face in ½ - 1h, depending a bit on where you camped. The slope gets steeper and steeper until you're at snow-covered ice-slopes.
The beginning of the actual climb at the face starts with steep ice at 70 -75 degrees for approx. 40-50 meters. It then flattens out a bit to 55 -65 degrees.
After this flatter section, it once again gets steeper and continues at 70-80 degrees most the way to the rock pyramid.
You can bivaq on the left hand side of the pyramid on a small snowy platform. It can be extremely windy here and also check out the snow quality carefully. The best places are very close to the rockface, but be sure there are no hidden melt-off holes.
The rock pyramid can be attacked along a couple of different routes, but the standard is following the narrow couloir just above the level snowfield on the mountains left flank.
The last part is steep rock climbing in exposed surroundings. The first part of the couloir is best attacked on the ice. After a short pitch, you arrive at a vertical section with hanging ice. On the right, the rock-chimney offers a good alternative, but be careful of loose rocks. On top of the chimney there are at least two places were the belayer is well protected.
Back down in the couloir again, some easy snow and ice climbing takes you to the crux. It looks horrible, but there are ok places for both hands and feet all the way, even though surface ice can complicate things a lot.
The climb continues in a mix of easy but very exposed scrambling. There are two steps on the way that have to be climbed. One of them is quite tricky. The last meters to the summit is a snowy walk, but be very careful, it's airy!
It can be climbed in one day, but you have to be fast, acclimatized and experienced. I was told, many climbers camp underneath the rock pyramid, climb it the next day and then all the way down.
3-4 rock pitons.
A few nuts.
One or two mid-sized friends.
2 snow stakes.
4 long ice screws.
If you attempt a route like this one, you are for sure able to add the rest of gear (slings, fig 8, karabiners etc.) to your liking.
Walking sticks and of course all the normal gear you'll need for glacier/snowcamping and being in potentially very cold, windy and exposed surroundings.