[BUG] can't rectify dual of rectified tesseract
Posted: Sun Dec 25, 2022 9:34 pm
rectified dual of rectified tesseract is in here: https://bendwavy.org/klitzing/incmats/o ... 3oc_zx.htm
It fails for the reason given in the error, no edge-tangency sphere. For rectification to work, edges are required to all be the same distance from the centre of the model. The points where edges are tangent to a sphere with that radius will be used as new vertices. With this condition, new faces are guaranteed to be planar and new cells corealmic. In 3D it also ensures the same result whether starting with the base or the dual, and that new faces lie in the same planes as the dual faces.
When the condition is not met, there may be cases where the result could still work, but wouldn't be as nice. Eg in 3D if the new faces are triangles, then they're sure to be planar, but may not lie in the same planes as the dual faces.
I'm not sure the situation in your case, but the edges are certainly at different distances from the centre. I notice your link says it "qualifies as rectification" rather than "is the rectification", so I figure maybe it qualifies topologically but maybe not geometrically.