The building formerly known as pyramid

It's been ages. I know. shhh.

So anyway, I've been thinking and rethinking the pyramid. If you don't know what that is, clicky the tags.
There's 2 huge problems with it: first of all, it was supposed to be able to sustain itself, but I'll need more crops for that. For this I need either space, which I don't have, or make room and I'd need sunlight, which the people living near the center of every city blocks wouldn't have.
So I decided to forget about the plants for a sec and focus on the sunlight. I came up with 2 solutions: first of all, I'm thinking about leaving a gap between floors, about 10 meters deep. This would allow for some sunlight to reach inward. Still, on this magnitude, this wouldn't allow for much sunlight to reach the center parts, and noone wants to live in perpetual darkness. No non-fungi, I mean. So I'd need some sort of sunfilter for the roofs. Basically, every 'empty' floor would be tiled with mirrors, and with a tightly regulated schedule, those panels would 'leak' sunlight onto the middle floors, then the side ones, and so on and so forth. I have the schedule here, but it needs work and I am far too lazy to copy it.

Second option would look a lot more aesthetic, but is far more difficult to achieve in real life. I doubt we have the materials to build this kind of thing without it falling over. I'll draw it in 3D sometime soon, because drawing it on paper is almost impossible.
In essence, it's the same thing it was before, a pyramid in 8 pizza slices, but in a spiraling double-helix-shape. This would give every single floor sunlight from above, and everyone living on the side would have a magnificent view (so you can charge extra for those rooms :p). Every floor now has only two slices, instead of eight, so it would reduce their overall cramming-potential. On the other hand, we don't need more skyscrapers and I like my thingy better, so there.
I'd make sure every (other?) floor has one of those two slices developed as agricultural estate. They're large enough for crops or even herds, and it would allow for the structure to support itself.

My biggest problem is supporting this beauty. After all, the pyramid kinda supports itself. It's a pyramid for chrissakes. But I'm afraid that the spiral will HAVE to be disfigured by either a gazillion support beams, or a single huge one per pizza-slice. Neither seems attractive.

The final thing is whether or not I should let them spiral, or just go up and stop, like a double helix. The spiral would be easier to support, but I don't know.

Oppinions/Architectural advice?