Hi Mel, I had the book in about 1962 i reckon, in melbourne Australia. I had no idea what it was about, just a weird story.
The full name was "Tom Atom and His Magic Domes". The characters were like smileys with arms & legs sticking out. They went on a big trek, climbed a mountain, then got into the domes where they played a weird game throwing lots of heavy balls at each other till the whole place got really hot & steam started to form & generate electricity to power peoples homes wasnt it wonderful. !.
I remember them getting to the foot of the mountain and climbing up on the toes. Non funny adult humour meant for kids but not really hitting the mark.
When I showed it to my year 10 maths teacher he asked if i was given a lot of things like that as a kid, i guess he figured it explained a lot about me. Probably the cause of all my problems i guess. if only i could remember who gave it to me so i could blame them!