Pentagonal Torus

Pentagonal Torus
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Type	Deltahedron
Rods	120 ×
Spheres	40 ×
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.

Other Versions

Wooden Panels

Related Links

• Lobel Frames