Algorithmically create block matrices

I want to create a block matrix out of square matrices with the following structure

H = [A B C D;
    B A B C;
    C B A B;
    D C B A]

Cleraly, if I was interested in only a 4x4 block, this would be enough. However, I'm interested in constructing such matrices out of a set of N square matrices A,B,C,D,E ... forming an N by N matrix of square matrices. Suppose I define

Matrices = [A B C D E];

What is the code I need to construct the corresponding 5 by 5 block matrix?

Answer 1

[Fangjun Jiang]

cat()

vertcat()

[David Cyncynates]

oh i see - cycle through Matrices and then cat. Thanks!