Guthrie's solid, composed of 2n parallelepipeds superposed as above show that we can find in space n domains (here each of them composed of two crossed parallelepipeds of same color) such that any pair of them always meet along a surface with nonzero area.

This proves that the situation is completely different from the situation of the plane where the maximum number of domains such that any pair of them meet along a curve with nonzero length is equal to 4.
 
 

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© Robert FERRÉOL 2017