The Open Trapezoid Twist (also just called Trapezoid Twist) is a moderately common twist and is usually one of the first mixed-depth twists that a new tessellation folder learns.
Crease Patterns and Folded Forms
Animations
Animations by Ben Parker using Origami Simulator
Uses in Tessellations
Open trapezoid twists are folded starting from an equilateral triangle grid and the folds that outline the trapezoid itself are not on grid lines.
The twist can be folded with or without precreasing these folds, depending on the expertise of the folder.
This twist is lesson commonly used in origami tessellations since it uses multiple pleat depths and so does not fit in the most common tilings.
Here’s some examples of tessellations that use this twist:
Video Tutorial
History
The open trapezoid 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!
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