Notes before you start: You experiment with different types of beads like seed beads, bugle etc. The pictorials are illustrated with spaces between beads for a clearer direction, in the actual beading, there should be no spaces. You can use a string and needle or Nylon fishing line (0.25mm) without the needle.
Two different stringing techniques for triangle weave are featured: Triangle Weave using double thread stringing method
String 3 beads and cross the both ends of the string at the last added bead.
Continue to add two beads at time and cross both lines through the last added beads. (note: if you choose to cross the bottom bead - as shown in the picture - then do the same by crossing the bottom bead for all the beads added in future)
The different colors represent each step of added beads - first 3 (green) then 2 (blue), 2 (green), 2 (blue), 2 (green), for the final step - 1 blue bead and cross both lines back through this bead.
Continue by repeating step 2 and 3 but add 2 / 2 / 2 / 1 beads (total 7 beads) as shown.
Continue by repeating step 2 and 3 but add 2 / 2 / 1 beads (total 5 beads) as shown.
Continue by repeating step 5 three more times and end off the last step by adding (red bead) 2 / 1 (total 3 beads as shown).
By now you should be getting the momentum so continue to expand this triangle weave stitch until you achieve what you have in mind.
I have used this stitch for projects like: Beaded Ring ; Pendants ; Beaded Coaster ; Bracelet