I wondered if someone could explain what properties define "pyramid games"? Someone suggested that I have a look at icehousegames.org but it's not clear to me from that site what are the the things that those games have in common. (Obviously, I assume they involve at least some pieces that are shaped like pyramids, but there are lots of interesting features mentioned in the description of Icehouse and it's not clear to me which (if any) of these are to be found in other games of that type.)
The only true property that these games share are that they all use one or more "stashes" (set of 15) of pyramids sold by the game company Looney Labs. Given that the pieces themselves come in three sizes, they can be stacked on top of each other or nested inside of each other. This, along with the fact that they are pointed, gives rise to a weak theme of directionality through the games, but really any game that has been created using these pieces can call themselves a pyramid game.
There is a fertile area of game development surrounding these pieces, so there is a large number of official and unofficial games played using these rules. Icehouse was the original, but really isn't that strong of a game and isn't a good indicator of how the pieces are usually used. I would suggest looking at a few of the old favorites to get a feel for the type and style of games the the pieces are involved in: