We seem to have three very different versions of Orthanc from Tolkien's pictures:
First a very 'man-made' Orthanc, but that was dropped quite soon, and is obviously incompatible with the book.
There is a description of Orthanc in the "The Road to Isengard", TTT:
To the center all roads ran between their chains. There stood a tower of marvellous shape. It was fashioned by the builders of old, who smoothed the Ring of Isengard, and yet it seemed a thing not made by the craft of Men, but riven from the bones of the earth in the ancient torment of the hills. A peak and isle of rock it was, black and gleaming hard: four mighty piers of many-sided stone were welded into one, but near the summit they opened into gaping horns, their pinnacles sharp as the points of spears, keen-edged as knives. Between them was a narrow space, and there upon a floor of polished stone, written with strange signs, a man might stand five hundred feet above the plains.
"Riven from the bones of the earth" seems to suggest (to me) that it is not as 'decorative' and spiky as in the movie, and more 'streamlined'. In that case, 'many-sided stone' probably means that it looks like a regular polygon seen from above.
Here we have a natural design, looking rough and stony
Then, this is what Tolkien drew on front cover of The Two Towers, which was then published:
I would say the latter one is what it looks like, since the walls are described as being 'smooth', the walls were black, and it was published.
I think the movie model is not natural enough, since all of Tolkien's designs seem very organic, except the first.
The second is very rough, but not in the 'spiky' way the one in the movie is. Also, the spikes are part of the building, and not 'added' on top.