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This video shows how to build Jessen's Orthogonal Icosahedron with edge length 6 using 1522 magnets and at the end of the video with edge length 5 using 826 magnets.
To build the shape with edge length n, with n greater or equal to 2, the required amount of magnets N is 1/3(28n^3-42n^2+2n+18).
n, N
2, 26
3, 134
4, 382
5, 826
6, 1522
7, 2526
8, 3894
9, 5682
10, 7946
11, 10742
12, 14126
13, 18152
14, 22882
15, 28366
The shape with edge length 3 is quite difficult to build and I don't think it is possible to make the shape with edge length 2.
Zen Magnets are available at zenmagnets.com/.