Here is an example I get a strongly distorted tori which is derived from a parent torus with D
5d symmetry, even though the correspondent connectivity graph contains correct number of pentagons and heptagons. The Euler formula is also satisfied.
I also have another example derived from D
5h symmetry. Here I simply moved pentagons' position one unit, I am unable to connect upper and lower branches completely.
These examples tell us that even though the number of distinct tori grows exponentially, most of them are highly strained and strongly distorted away from toroidal shape.
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