I tried this in Alameda (SF Bay, Zone 9b) for a couple of years. I used 1x6s with corner brackets that I bought at the local hardware store. (bought 8' and 6' lengths of lumber and had 1 cut apiece on them to build the squares and then sunk a bottomless round plastic container on top of the 3' square section to form the "crown").

Successes: lettuces and spinach at all levels of the tiers (wonderful, flavorful and handy for months), strawberries at top two levels of the tiers, parsley, thyme, oregano at all levels of the tiers, tomato at the top level (only planted it like that on one pyramid), eggplants at the bottom tier (was based on a concrete walkway). round carrots (but after tasting 'em -- why bother?), zucchini when planted by itself in the pyramid with only green beans as the top tier --the zuchini couldn't swallow the highflying green beans and the green beans didn't seem to be affected by the mildew that assaulted the zucchini, which didn't seem to mind the mildew at all.

Failures: Tomatoes at anything other than the top tier, no cukes at all (mildew [which spread to everything else in that pyramid] and rampaging over everything else), zucchini had to be pulled because it ate up all the space and was killing off everything else, snap peas (trellised out of the top tier) got mildewed and never fruited (not to mention shading the back side...)

Caveat on strawberries in small spaces: Strawberries were nice in the pyramid, but frankly in the same timespan, I built a "strawberry tree" from, I think, a Sunset, article, with chicken wire and moss making a cylinder coming up out of a 15 gal pot -- 14 strawberry plants in the cylinder tower and 5 around the base -- they were outstanding! each berry huge, sweet and red and far more flavorful than anything in the pyramid. Enough for breakfast for two every morning through the season. That was a neighborhood wonder for all three years -- I willed it to my next door neighbor when I moved and I think she got 2 more years out of it (just rooting the runners into the tower and pouring a manure tea through during the winter). I think that's a better option for the berries.