The Open Triangle Twist (also called Spread Triangle Twist, or Triangle Spread) is one of the more common twists done on a triangle grid, and usually one of the first that a newer folder learns.
It looks similar to the closed triangle twist, but there is an area on the backside that looks like negative space (is only one layer thick) that allows for interesting backlighting contrast.
Crease Patterns and Folded Forms
Animations
Animations by Ben Parker, using Origami Simulator
Uses in Tessellations
Open triangle twists are folded starting from a regular triangle grid. The mountain folds that form the triangle itself are not in the grid. The twist can be folded with or without pre-creasing those folds, depending on the expertise of the folder.
They are one of the most widely used twists in origami tessellations.
The simplest two patterns that use only open triangle twists have left- and right-handed copies on the same or on opposite sides of the paper, respectively.
Here’s some examples that use this twist with other twists too:
Video Tutorial
History
The open equilateral triangle twist was not present in any of Shuzo Fujimoto’s publications and is present in Eric Gjerde’s Origami Tessellations.
If you have additional information about the history of this twist, please share it in the comments below!