There are as many types of cactus or more than there are types of wood! What kind of cactus are you going to carve? by the description, I would assume a saquaro and you could do one out of 4x4's glued...you might want to do a google search on them, because they don't look like what people think they look like up close. You could also carve beaver tail cactus and use 2x2's and 1x4 or 6...as I said, lots and lots of different cacti...Dave
