The Open Mixed-Depth Square Twist, also called Mix Square Twist, is an advanced twist used in origami tessellations.
Crease Patterns and Folded Forms
Animation
Animation by Ben Parker, using Origami Simulator
Uses in Tessellations
The mixed-depth square twist is folded starting from a regular square grid. The mountain folds that form the square 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.
Since this twist uses different pleat depths for the different pleat directions it requires special consideration for use in tessellations and can create some unique effects not available with other square twists.
Here’s some examples of tessellations that use this twist:
Video Tutorial
History
The mixed-depth square twist dates back to at least the early 2000s.
If you have additional information about the history of this twist, please share it in the comments below!