Alright,
with much time and an extensive amout of google search I managed to cobble a working QOpenGLWidget program together.

I used this official Qt-Example as a basline:
http://doc.qt.io/qt-5/qtopengl-cube-example.html

here is the combination with my Tesseract code
https://github.com/DeiVadder/Tesseract-Challenge-OpenGL

It's working, yeah me!!, but I have the feeling that it's far from ideal. I'm just glad I managed to draw something in 3d.

Anyway, closed and solved.