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Pentagonal Torus

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Pentagonal Torus
Pentagonal torus
Rods 120 × Geomag rod icon
Spheres 40 × Geomag ball icon
Author Amafirlian 08:29, 15 August 2007 (UTC)

(0,5,0,30,0,5)-deltahedron forming a pentagonal torus.

Because the topology is not that of a sphere but that of a torus the relation between the number of spheres with valencies 3, 4, 5, 6, ..., (n3,n4,n5,n6,... ) is given by

3\,n_3+2\,n_4+n_5-n_7-2\,n_8-3\,n_9-4\,n_{10}-\cdots -(k-6)\,n_k-\cdots=0

It is completely rigid, and highly reminiscent of Alain Lobel's frames.

Counting: There are four rings: the inner ring has 5 balls, the two middle rings 10, and the outer 15, for a total of 40. Rods have additional supports between the rings, and extra 10*8=80 rods, for 120 total.

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