Tuesday, December 12, 2006

Strongly distorted tori

Here is an example I get a strongly distorted tori which is derived from a parent torus with D5d symmetry, even though the correspondent connectivity graph contains correct number of pentagons and heptagons. The Euler formula is also satisfied.

From Craft Projects


From Craft Projects


I also have another example derived from D5h symmetry. Here I simply moved pentagons' position one unit, I am unable to connect upper and lower branches completely.
From Craft Projects


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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