Will an umbilic torus intersect itself?

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In the below two images you see one with three lines leaving point A each 120 degrees apart and a umbilic torus made from twisting a triangle around a circle.

I have tried to construct an umbilic torus with, rather than a triangle, the shape below. I am doing this with the intent of investigating, if utilizing the shape below, can you bring the umbilic torus diameter to a length infinitesimally larger than the length of segment A:B without causing the umbilic torus to intersect itself.

Unfortunately my skills in blender are not adequate enough for me to create this and I do not have any other software on my computer that would allow me to.

Does anyone know another way of answering this?

enter image description here

http://www.mathconsult.ch/static/pubs/illumath/IME22.gif

http://www.mathconsult.ch/static/pubs/illumath/IME22.gif