Inherit the Stars by James P Hogan was published in 1977 and was the first book in the Giants trilogy, which then became the Giants series when a further two more books were added a few years after.
The artwork here is by Darrell K Sweet who has done yet another fantastic cover inspired once again by the design of the 2001 A Space Odyssey costumes. I'm becoming a big fan of DKS. So much so that he gets his own label here on my blog.
You will of course have noticed that the image has been flipped for use on the book cover....or not! The other image is a scan from a sci-fi mag and I'm actually unsure which is the original version. Ah well! Either way works for me.