One of the new BUNGCO engineers was
fired from LEGO for his unconventional
ideals regarding toys. This is his first
acceptable product: the Pyramidal Lego.
These symmetric shapes require a
different approach to construction, and
have a sharp point pointing up no matter
how they are left
lying around in the dark,
on the rug in front of the bathroom door.

So, four sided pyramids, but how would the indentions/protrusions be organized on the faces? Some all indents, some all protruding, and some in various ratios of the two morphologies? (I think that would be best, leaving all options open).

<aside>A Lego that crumpled under a certain amount of pressure would be nice.</a>

A "pyramid" is usually a square base with 4 triangular sides, as done by Egyptians and all. But, according to Wikipedia, the defining feature of a pyramid is the triangular sides meeting at a point on the top. [ldischler] is right, and [bungston] is right, and my earlier question was silly--a tetrahedron IS a pyramid. Cheop's pyramid is a square-based pyramid.

If you were to pick up a little plastic 'ptian pyramid, you could say that it is an irregular solid with five faces. If you were to step on one, it would hurt, depending on which side is on the floor. But it doesn't hurt as much as it could.

A tetrahedron is the only regular, Platonic solid that has //a sharp point pointing up no matter how they are left lying//. The caltrop, of medieval fun and fame, is a 4-pointed derivative. And stepping on a caltrop is what poor [bungston] is flashing back to.

I raged around the search engines for a while, and found a few obscure attempts to make a tetrahedral Lego-oid toy, but none for sale as toys. I'd like a set, please.

One design had a funny clicky joint like Legos, that supposedly worked as both an inny and an outy, centered in each face. The chemistry-set design had a magnet in the middle of each face, that supposedly always worked with the all others in the set, with no north-south issues.

I propose a Lego-like inny-outy joint, with an inny on two faces of the tetrahedron, and an outy on the other two faces. I haven't worked that out clearly, yet, so that may be a bad idea.

Yes, symmetric and tetrahedral is good for design. But, competitors are going to come out with 5 sided ones, and it's going to sting a little, I'm afraid. Also, have you considered the indention/protrusion issue?

The connection issue using Lego-like bumps is actually pretty easy. Just think rotational symmetry. Have three bumps and three holes on each face. Arrange them as points of a hexagon, alternating holes and bumps. Have three of the sides of this hexagon parallel to the sides of the triangular face. Note that it is not symmetric in reflection. When the face is reflected and put on top of itself (as when connecting two pieces), all bumps line up with holes.