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a) train Zermatt - Rotenboden. Follow the broad summer track either to its end , or descend directly onto the Gornergletscher (blue paint marks) and traverse the glacier towards the hut (waymarked with flags).
b) train Zermatt - Gornergrat - Stockhorn
c) On foot from Zermatt via Rotenboden. From Zermatt follow the road then the footpath, (signposted Gornergrat) passing by Riffelalp and Ridfelberg until Rotenboden, then follow a).
d) From Zermatt by the Gornergletscher
Go up the moraine and follow a cwm, then a snow bulge to the Obere Plattje (3109m), Go up a 100m slope at 35/40°, trending left near the top. Go up easier angled slopes keeping to the right of the seracs, often badly crevassed, best to be roped up. Go up the snow bowls to reach a flat section at 4100m. (Until this point the route is the same as for the Dufourspitze). Go up one of the two glacial ramps on the left to reach the Silbersattel, 4515m.
From the Silbersattel climb the snow/ice ridge, maybe corniced , then easy mixed to the summit (4609m)
As for the ascent, but without passing by the hut, then by the Gornergletscher and Furi (until the start of May, later in the season it is better to return via Rotenboden.)