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Ice-sheet development in Antarctica was a result of significant and rapid global climate change about 34 million years ago. Ice-sheet and climate modelling suggest reductions in atmospheric carbon dioxide (less than three times the pre-industrial level of 280 parts per million by volume) that, in conjunction with the development of the Antarctic Circumpolar Current, led to cooling and glaciation paced by changes in Earth's orbit. Based on the present subglacial topography, numerical models point to ice-sheet genesis on mountain massifs of Antarctica, including the Gamburtsev mountains at Dome A, the centre of the present ice sheet. Our lack of knowledge of the present-day topography of the Gamburtsev mountains means, however, that the nature of early glaciation and subsequent development of a continental-sized ice sheet are uncertain. Here we present radar information about the base of the ice at Dome A, revealing classic Alpine topography with pre-existing river valleys overdeepened by valley glaciers formed when the mean summer surface temperature was around 3 degrees C. This landscape is likely to have developed during the initial phases of Antarctic glaciation. According to Antarctic climate history (estimated from offshore sediment records) the Gamburtsev mountains are probably older than 34 million years and were the main centre for ice-sheet growth. Moreover, the landscape has most probably been preserved beneath the present ice sheet for around 14 million years.