Rings needed: nine 16 ga 5/16", six 18 ga 1/4", three 18 ga 3/16" and nine 18 ga 5/32"
Close six 18 ga 1/4" rings and connect them in pairs of two with 18 ga 5/32" rings as shown.
Attach the ends with another 18 ga 5/32" ring.
Put a 16 ga 5/16" ring around one of the smaller rings so that goes in between the 18 ga 1/4" rings. This takes a bit of negotiating :).

Here's the side-view:
Add two more 16 ga 5/16" rings to fill up the pattern; this is tight and it needs to be so to make the piece rigid.
Put two 16 ga 5/16" rings through one of the 18 ga 1/4" ring pairs as shown.

From the side:
Repeat on the other sides.
Link the just added 16 ga 5/16" rings together at each point with two 18 ga 5/32" rings:
Loop a 18 ga 3/16" ring through the two rings you added; make sure the ring will also go through the 16 ga 5/16" 'base' ring and between the two large, vertical rings.

Seen from 'above':
Repeat, and you have your triangle :).
Triangle design by Lari Nieminen, this tutorial by Paula Kosunen
www.pieceofmaille.com