Flyback winding question

[RoamingD]

Hello, I got hold of this pair of E type ferrite cores from an old tv main board (it's not from the line flyback transformer that drives the crt)
My question is, can I rewind this transformer like I drawn in the picture? The gap is only in the middle, if I rewind it like I shown, should I add a layer of tape between one of the sides like in a traditional crt flyback?

[klugesmith]

Of course you can wind it like that.   
Whether it can meet your electrical requirement depends on what you want to do.
Transformer? Flyback converter?
In any case, it would be an inefficient use of the core mass.

[RoamingD]

I would like to make a small hv ac power supply (use it as a normal tv flyback) just for playing with arcs or maybe a multiplier in the future, if I would get 3 cm arcs I would be very happy  but regarding the gap, should I cover one contact point with a piece of tape?

[davekni]

In any case, it would be an inefficient use of the core mass.

Not only inefficient use of mass, but the unused center posts will shunt magnetic field, further reducing field that gets from primary to secondary.  If you continue that way for either flyback drive or ZVS drive, yes, outside leg(s) need gapping.

That core is intended for windings around center.  Will work better if you wind secondary around center and two identical primary windings, one around each leg.  Primaries can be wired in series or parallel depending on desired primary impedance.  For this configuration, no additional gap is needed beyond existing center post gap.  Primary windings need to generate flux through center, not in a loop around outside legs.  If both are wound clockwise from bottom to top as viewed from top, then parallel the two top leads and the two bottom leads.  Or series connect one bottom to other top lead.