"And is it better for the female plant to be the tetraploid or the diploid?"

I don't know about zinnias, but in breeding seedless watermelons the tetraploid has to be the female plant. In the linked page scroll way down to the section "Seedless Variety Development."

Here is a link that might be useful: NC State Univ Watermelon Breeding

Mistercross,

Thanks for that information. This last year, I tried the cross both ways and hopefully will have some results this year. This coming year I will also be using some of the tetra zinnias from Burpee. This last year I used only "State Fair."

Tetra zinnias have their own special "look", which I am not particularly fond of. The petals all tend to be cupped like spoons, which exposes to view some of their bottom surface, which doesn't look very good.

So I am a bit skeptical about whether I will like any triploid zinnias, even if I am successful in producing them. But I plan to continue the experiments in a kind of low priority way. I expect better results from my crosses between various diploid zinnias.

MM