What book is this?

I’m trying to recall the name of a science fiction book I read as a kid, but I can’t remember enough about it to have any luck on Google. It’s about a caveman named Flint (I think) who lives on a caveman planet. He gets talked into visiting different planets for some sort of diplomatic reason.
One of the planets has three sexes, with one being a catalyst for the mating of the other two.
One planet is inhabited by people who look like hershey’s kisses on mouseballs. This society thinks circularly instead of linearly, and has some sort of tarot card symbology also.
I’m trying to get my daughter to read more, and I hope someone here will recognize this plot. Thanks!

That’s Piers Anthony’s Cluster series; one of his better ones as I recall. Flint the cave man is that way because his world was settled with “mattermission”, a form a teleportation which is extremely expensive ( so they didn’t send much in the way of tools ). There’s another form of transport that sends someone’s “Kirlian aura” as a sort of possession of a being on the targeted world, but it decays over time until the traveller has to return to his/her own body. Flint gets recruited because he has a freakishly strong aura, and can thus last longer.

Ugh, I screwed up my reply- trying again.
Thank you, that’s it! I didn’t realize it was Piers Anthony. I saw a whole shelf of PAs at the thrift store the other week, but didn’t bother to look through them cause PA seems to be seen as the Harlequin romance of sci-fi. Although that would be right up my daughter’s alley- she’s a kinda slow reader and prefers young adult fantasy.

He’s best described as “uneven” I think, at least with his older stuff. It ranges from quite good to not good at all. I haven’t read his newer stuff, so I won’t comment on it.