## Thursday, May 11, 2017

### More right angle tetrahedra

I'm still learning a lot playing with tets (tetrahedra) that include right angles.  The first picture here, which I used in an earlier post, shows the kind of ring structures I've been building for a while with equilateral triangle tets.  The inner ring is a row of triangles alternating point-up and point-down.  Then each of these triangles becomes the base of a tet.  Then, for the outer edge I join all the top points of the tets.
In the last couple of posts I switched from equilateral triangles to right angle ones.  The inner ring is a row of right angle isoceles triangles that alternate hypotenuse-up and hypotenuse-down.  Then I went on to see what structures I could generate.
But the problem with both of those structures is that all the tubes on that inner rim are at an angle
to the overall structure, so you can't easily break up the ring and put a clasp in, which you sometimes want to do.  So I started thinking about making the inner ring out of right triangles, but using the right angle so that you have tubes that are perpendicular to the overall direction of the ring.  I don't know if that makes sense, and I was in a hurry to write this down, so my picture may not show things well enough.  But I think this is going to be useful.  Here I won't be using a clasp; the plan is to make 6 (possibly 8) of the small shapes, with the big one at the bottom.  It'll be a  pretty large necklace--the big shape is over 4" across and the small ones are about 2 1/4" across.  So it should have a lot of impact.  You can't tell too well from my bad picture but there's a sort of pinwheel of orange tubes on one side and yellow tubes on the other.  I'll probably put 1 color on top for all the small shapes and the other color on top on the big one.  Stay tuned.