Hollow Cuboctahedron Tutorial (Zen Magnets)

This video shows how to build a double-thickness hollow cuboctahedron out of Zen Magnets. The technique is an adaptation of Mathnetism’s hollow diagonal cube technique (see    • Hollow Diagonal Cube (Zen Magnets)  ,    • TUTORIAL Hollow Diagonal Cube (Zen Ma...  , and    • Mathnetism's Hollow Diagonal Cube (Ze...  ). For even edge lengths n = 4 and larger, the hollow cuboctahedron uses N = 20n^2-60n+54 magnets.

N is the difference between the number 3(10n^3-15n^2+11n-3) of magnets in a solid cuboctahedron of edge length n and the number 3[10(n-2)^3-15(n-2)^2+11(n-2)-3] of magnets in a smaller solid cuboctahedron of edge length n-2. This smaller cuboctahedron is the size and shape and number of magnets of the hollow space inside of the hollow cuboctahedron.

Building the hollow cuboctahedron actually requires more than N magnets, magnets that you cut off at the last step. The number of extra magnets required is a few magnets shy of the number M = 6n(n-1)+1 of magnets in the triple-thickness slab used to build the top and the bottom of the cuboctahedron. You can cut off these magnets as you build the shape, but it’s trickier to complete this way.

n, N, M
4, 134, 73
6, 414, 181
8, 854, 337
10, 1454, 541
12, 2214, 793
14, 3134, 1093
16, 4214, 1441
18, 5454, 1837
20, 6854, 2281

In the video, I show completed cuboctahedra with edge lengths n = 4, 6, 8, 10, 12, and 14, and I build the shape from start to finish for n = 8 (854 magnets). The shape can be built in sizes larger than n = 14, but their angled walls and vertices are less stable than for smaller sizes.