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Producing a matrix from particular calculations from 3D cell array (of vectors)

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Dear all, I was wondering if there is a way to produce a matrix consisting of distance between all possible combination of two vectors defined in 3D cell array of vectors.
For example, suppose I have a 3x3x3 cell array, where each cell contains a vector with x, y, z coordinates. I want to make a matrix containing Euclidean distance between every single possible combination of vectors defined in 3x3x3 including its own (=27 vectors), which the same vector pair is going to produce zero. So in the end, we should get 27x27 matrix with zero for diagonal elements.
What I thought of was using "for i = 1:3" commands to index particular vector, and use them over and over again to define the 27x27 matrix but that seems like a very inefficient thing to do.
Is there a more efficient way to do this?
Thank you.

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