Mathnetism's Hollow Diagonal Cube (Zen Magnets)

This video describes how to use Zen Magnets to build a hollow diagonal cube using Mathnetism's ingenious technique (see    • Hollow Diagonal Cube (Zen Magnets)   and    • TUTORIAL Hollow Diagonal Cube (Zen Ma...  ). The shape has double-thickness walls and is amazingly strong. For edge lengths n equal to 2 or larger, the shape requires a total magnet count of N = 24n(n-1)+14, giving:

n, N
2, 62
3, 158
4, 302
5, 494
6, 734
7, 1022
8, 1358
9, 1742
10, 2174
11, 2654
12, 3182
13, 3758
14, 4382
15, 5054
16, 5774
17, 6542
18, 7358
19, 8222
20, 9134
21, 10094
22, 11102
23, 12158
24, 13262
25, 14414
26, 15614
27, 16862
28, 18158
29, 19502
30, 20894

Shown in the video are cubes of edge length 5 (494 magnets) and edge length 20 (9134 magnets). The magnet count equation was derived by subtracting the magnet count of a solid diagonal cube of edge length n-2 from that of a solid diagonal cube of edge length n, that is, by hollowing out a solid cube and seeing how many magnets are left. For more information about solid diagonal cubes, see    • The Definitive Diagonal Cube Tutorial...  .