FATMAP difficulty grade
This is as good as low-grade mountaineering gets, with a 4000 metre summit, epic alpine views and a charming mountain hut all featuring.
Start by riding the Klein Matterhorn lift from Zermatt all the way to the top station at 3883 metres.
Incidentally, this is the highest point in Europe which can be reached using a tramway or gondola. Follow the ski draglift line south out of the station and then, when the draglift ends, swing around to the east and cross the glacial plateau which leads to the foot of the Breithorn's south face.
Climb the south face via easy snow slops and swing onto the summit.
The view is utterly staggering, with the Matterhorn taking centre stage and the other 4000 metre peaks of the Valais laid out beneath you.
Retrace your steps back down the south face and then head east-southeast across a spectacular glacial shelf in the direction of Castor and Pollux.
Once immediately west of Pollux, turn south and descend to the Guide d'Ayas hut.
The exact route across the glacial plateau will depend on the current state of the glacier and the location of crevasse zones.
Although the terrain you're travelling through is easy, experience of moving through serious glaciers is essential to safely reach the hut.
Once at the hut, enjoy the superb hospitality and the fabulous sunset from the terrace.