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I'd like to make a software on Python with a GUI for 3D visual editing of meshes. That's why I ask the question. I suppose at least one mesh editing library is used. And at least one 3d visualization library is used.

Please do not answer to use blender or other existing OSS.

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    I'm voting to close this question as off-topic because it is similar to asking how a package works – Mick Aug 20 '18 at 7:26
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While you don't want the answer to be blender, it is the answer. All of the mesh editing and display is written in C/C++ and is part of blenders source tree, the external libraries blender uses are for image formats, simulations and rigs.

OpenGL is used for the screen drawing but that offers no help for storing and editing mesh data, it is purely screen drawing commands.

Blender does use python to define its UI layout. It is possible to fork blender and modify python scripts to get a custom UI that uses blender behind the scenes.

Makehuman is a 3d program written using python and pyqt, that might be a source of inspiration for you.

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