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Zermatt needs a full day from Lake Thun. Start among the old wooden houses in the village and look for the Matterhorn when the clouds lift. Fast trains via Visp can put it close to two hours away, though engineering work can lengthen the trip. Drivers leave the car at Täsch and continue by train.
Adding the Matterhorn Express and the lifts towards Matterhorn Glacier Paradise takes more time: first the walk to the valley station, then the ascent and descent. Work backwards from your return train before committing to the mountain ride. The Glacier Express is a separate train journey.