### 3x3x3x3 (simple) magic hypercube

Read on webpage 'Magic features' that a (4D) 3x3x3x3 cube consists of 3 cubes which are put over each other. If you put the levels of the 3x3x3 cubes next to each other, it looks like a 9x9 magic square with a specific structure. In 3 steps you can construct all 3x3x3x3 (simple) hyper cubes:

Step 1
Choose two the same or two different 3x3 magic squares out of the eight 3x3 magic squares.

 2 9 4 2 7 6 4 9 2 4 3 8 7 5 3 9 5 1 3 5 7 9 5 1 6 1 8 4 3 8 8 1 6 2 7 6 6 7 2 6 1 8 8 3 4 8 1 6 1 5 9 7 5 3 1 5 9 3 5 7 8 3 4 2 9 4 6 7 2 4 9 2

Step 2
Choose two matching (for the 348 combination possibilities, see download) grids (see below all 28 grids).

 1a 1b 7 5 3 6 1 8 2 9 4 2 9 4 6 1 8 7 5 3 6 1 8 2 9 4 7 5 3 7 5 3 2 9 4 6 1 8 2 9 4 7 5 3 6 1 8 6 1 8 7 5 3 2 9 4 6 1 8 2 9 4 7 5 3 7 5 3 2 9 4 6 1 8 2 9 4 7 5 3 6 1 8 6 1 8 7 5 3 2 9 4 7 5 3 6 1 8 2 9 4 2 9 4 6 1 8 7 5 3 2 9 4 7 5 3 6 1 8 6 1 8 7 5 3 2 9 4 7 5 3 6 1 8 2 9 4 2 9 4 6 1 8 7 5 3 6 1 8 2 9 4 7 5 3 7 5 3 2 9 4 6 1 8 1c 1d 6 1 8 7 5 3 2 9 4 2 9 4 7 5 3 6 1 8 2 9 4 6 1 8 7 5 3 7 5 3 6 1 8 2 9 4 7 5 3 2 9 4 6 1 8 6 1 8 2 9 4 7 5 3 7 5 3 2 9 4 6 1 8 6 1 8 2 9 4 7 5 3 6 1 8 7 5 3 2 9 4 2 9 4 7 5 3 6 1 8 2 9 4 6 1 8 7 5 3 7 5 3 6 1 8 2 9 4 2 9 4 6 1 8 7 5 3 7 5 3 6 1 8 2 9 4 7 5 3 2 9 4 6 1 8 6 1 8 2 9 4 7 5 3 6 1 8 7 5 3 2 9 4 2 9 4 7 5 3 6 1 8 2a 2b 9 4 2 4 2 9 2 9 4 2 9 4 9 4 2 4 2 9 5 3 7 3 7 5 7 5 3 7 5 3 5 3 7 3 7 5 1 8 6 8 6 1 6 1 8 6 1 8 1 8 6 8 6 1 4 2 9 2 9 4 9 4 2 4 2 9 2 9 4 9 4 2 3 7 5 7 5 3 5 3 7 3 7 5 7 5 3 5 3 7 8 6 1 6 1 8 1 8 6 8 6 1 6 1 8 1 8 6 2 9 4 9 4 2 4 2 9 9 4 2 4 2 9 2 9 4 7 5 3 5 3 7 3 7 5 5 3 7 3 7 5 7 5 3 6 1 8 1 8 6 8 6 1 1 8 6 8 6 1 6 1 8 2c 2d 4 2 9 9 4 2 2 9 4 2 9 4 4 2 9 9 4 2 3 7 5 5 3 7 7 5 3 7 5 3 3 7 5 5 3 7 8 6 1 1 8 6 6 1 8 6 1 8 8 6 1 1 8 6 9 4 2 2 9 4 4 2 9 9 4 2 2 9 4 4 2 9 5 3 7 7 5 3 3 7 5 5 3 7 7 5 3 3 7 5 1 8 6 6 1 8 8 6 1 1 8 6 6 1 8 8 6 1 2 9 4 4 2 9 9 4 2 4 2 9 9 4 2 2 9 4 7 5 3 3 7 5 5 3 7 3 7 5 5 3 7 7 5 3 6 1 8 8 6 1 1 8 6 8 6 1 1 8 6 6 1 8 3a 3b 1 8 6 9 4 2 5 3 7 3 7 5 4 2 9 8 6 1 9 4 2 5 3 7 1 8 6 8 6 1 3 7 5 4 2 9 5 3 7 1 8 6 9 4 2 4 2 9 8 6 1 3 7 5 6 1 8 2 9 4 7 5 3 7 5 3 2 9 4 6 1 8 2 9 4 7 5 3 6 1 8 6 1 8 7 5 3 2 9 4 7 5 3 6 1 8 2 9 4 2 9 4 6 1 8 7 5 3 8 6 1 4 2 9 3 7 5 5 3 7 9 4 2 1 8 6 4 2 9 3 7 5 8 6 1 1 8 6 5 3 7 9 4 2 3 7 5 8 6 1 4 2 9 9 4 2 1 8 6 5 3 7 3c 3d 8 6 1 4 2 9 3 7 5 5 3 7 9 4 2 1 8 6 4 2 9 3 7