coan.net: I imagined you move as in Spider Line4 but you can connect 4 over the edges to win - so the Sphere just describes the scoring, not the placing. But that was just what came to my mind when I read "Sphere Spider Line4", I didn't think about it any further, I might be talking about something different from joshi_tm's idea.
joshi tm: I can imagine CL4 to be very interesting and playable. It would just make every column even in value, I don't know if this would give white more or less advantage, but I don't think I'd care too much ;) The L4 games all are in favor of white, but I like them anyway.
Cylinder Line4 is missing on BrainKing - let's get it! And in the end, Sphere Spider Line4 might be big fun too :)
joshi tm: Cylinder line4 would be interesting I think. With Sphere Spider Line4 I have the feeling that it would be even more unbalanced than Spider Line4 - but that is just a feeling, I can't back that up theoretically ;)