20x20x20 magic cube

 

A Nasik (= pandiagonal & pantriagonal) 20x20x20 magic cube does not exist. You can get a diagonal ór a pantriagonal 20x20x20 magic cube.

 

With a 20x20 magic square consisting of 2x2x proportional 10x10 magic square, you can construct a diagonal 20x20x20 magic cube.

 

I have constructed a 20x20x20 diagonal magic cube and 1/2 diagonals in each level and 1/2 diagonals and 1/2 (main) triagonals through the levels give 1/2 of the magic sum. It is a pitty that 1/2 pillars do not give the magic sum so the cube does not consist of 8x 10x10x10.

 

Luckily I succeeded in constructing a 20x20x20 diagonal magic cube, consisting of 8x poportional 10x10x10 diagonal magic cube.

 

With a special composite 20x20 magic square you can construct a pantriagonal 20x20x20 magic cube.

 

Using a pantriagonal 4x4x4 magic cube and a pantriagonal 5x5x5 magic cube there are three possibilities to construct a pantriagonal 20x20x20 magic cube: pantriagonal (1), pantriagonal (2) and pantriagonal (3).

 

I have also constructed a 20x20x20 pantriagonal magic cube consisting of 125 proportional pantriagonal 4x4x4 magic cubes.