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Assuming you're talking about doing this on EARTH, I think the core problem here is that the mountain would have to be insanely far from the Earth for the escape velocity to be small enough to achieve with a jump. A mountain couldn't even work because if it's a triangle shape, the base would be much larger than the size of the Earth itself. Even if you just had a super narrow tower, it would have to be so tall that it would be several times over larger than the thickness of the planet. I don't even think there's any material you could use to build a tower like that that would be structurally stable. A space elevator concept of carbon nanotubes maybe
