I'm the asinine one here* -- I'd figured you were above that.
>>>"the ground completes one side of each triangle"
I've been saying for about three months now that you cannot separate your fancy from "reality." Of course, in any sense of absolution none of us can do this, IMO. But your biases run much deeper than your ability to examine them, and any attempt to show you this (on my part, at least) has resulted in you repeating the same sorts of arguments -- arguments dependent upon your inability to step away from these biases.
Let's look at the challenge, stated thus:
"Can you arrange them to form four (4) identical equilateral triangles?"
"Them," of course, means toothpicks. The challenge does not say, "Can you arrange the toothpicks, plus imaginary things, to form four (4) identical equilateral triangles?"
The "triangles" at the bottoms of your pyramids are imaginary products of a natural, holistic bias. Of course, all of us can understand what you're saying, but my point isn't to criticize your imagination. My point is to criticize your ability to step away from this imagination long enough to logically examine it. In imaginary terms, this puzzle can resolve with as many triangles as one can imagine, by definition. I mean, think about the elaborate, tetrahedron-esque mini-table someone like Alan could imagine, even build, upon which to set these six toothpicks!
(1) You did not solve the puzzle (indeed, your "solution" contains no triangles whatsoever.)
(2) You think you solved the puzzle.
(3) You think you solved the puzzle because -- again -- you have elevated the products of your imagination to a level where they override "reality" outside of your imagination.
Essentially your "solution" is just another illustration of your inability to separate what you imagine from the rest of the world. THIS, I believe, is the reason you and I cannot get any further into my criticism of Ontology.
* - BTW, I'm sure Mike's being asinine too, though I don't bother opening his posts anymore.