Is there a function to fix edge length in Blender? I hope this question is clear enough. I am trying to create a 3D model of a tesselated origami model. What I want to do is translate a vertex and have the surrounding vertices translate such that edges connecting them to the translated vertex keep their original length.

Here is an image of the origami model:



Here is an image of the 3D model of the flat tesselated pattern:



I hope you can see here that I would like to translate the centre points of the concave hexagons (the vertices currently selected) and have the connected edges keep their length as if it was made of a rigid material.
For the specific case, You may consider using cloth simulation to preserve the edge length:

Step 1 to 3: Create Unit; mirror + arrays; Apply modifiers + coloring for convenience. (For existing model, you can ignore above)

Step 4: Select all poked vertices, CtrlG to add to a new vertex group, then CtrlH) to add a hook.

Step 5: Add Cloth simulator. use the vertex group as pins.

Step 6: Scale the hook while simulating (playing animation). Then AltC - 2 to convert the result. Finally, delete all unwanted faces.





Example file