Dr. Dome is pictured on the cover for Plastic Man 3 (March/April 1967), which is a bit of a shame, as it gives away his presence in the Drake and Mortimer story.
The tale begins with Mike DeLute and her mother at a shipboard party. We meet quite a number of men who are interested in her, but of course she only has eyes for Plas. One of those who expresses interest, the Duke of Wheelington, after being rejected, announces that he holds the patent for the wheel, and prevents anyone from using anything with a wheel in it.
Plas tries to stand up to the guy, and the Duke uses this as an excuse to place a multi-million dollar tag on any wheel usage. He has a family tree that goes all the way back to caveman times, using this as proof of his claims. It's all preposterous, and, in my eyes, not terribly funny.
Everyone blames Plastic Man for pissing off the Duke, and causing the situation. Mike DeLute's mother convinces her to marry the Duke so that he will waive the charges on them.
Plastic Man interrupts the wedding to claim that his ancestor invented fire, so anything made using fire belongs to him. That irrelevancy aside, he then undresses the Duke and exposes him as really being Dr. Dome. Who we knew had to be in the story because of the cover. The fire scene pictured closes out the unfunny story.