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From the hut proceed in the northern direction by the marked path. After half an hour one path deters left to the Detmolder Grat, while we proceed in the same (N) direction. Soon the path gets quite lost among big rocks and you follow just rare red marks and cairns. So you approach the steep wall below Steinerne Maennln (Stone Men), two big granite towers on the SE ridge of Hochalmspitze. Steep snow (crampons, ice pick!) brings you high up, but the last, almost vertical part you must climb over rocks. Good steel ropes help you over, which is especially important in spring, in times of tour skiing, when they enable skiers to come down that wall relatively safely.
Reaching the East ridge the world changes completely. On the other side, there's a vast glacier and the ridge to the summit of Hochalmspitze looks easy.
But at the beginning it still requires some climbing. Just at the beginning there is a narrow ledge, actually the top of icy slope, finishing some ten meters below in a crevasse. After it, red marks take you to the ridge again, you soon reach the next tower and go left of it. Then difficulties end for some time.
A broad rocky ridge brings you to the last steep tower. The route goes right, find its weak points and with a help of a steel rope soon brings you on the top of it. Now you have only an easy walk to the fore-summit (Schneeige Hochalmspitze - Snow Peak).
The main summit is just a few minutes away. If the ridge is dry, climbing it is easy (UIAA I degree), but on some parts it is quite exposed.
You usually return by the same route, of course you can make any other combination on the mountain.
Ice pick, crampons. Rope if somebody is not used to overcome exposed passages, in late summer also, because of end crevasse and general conditions on the glacier.