Hadamard matrices

In Ian Stewart's book "Die letzten Rätsel der Mathematik" (ISBN 978-3499616945), at the end there is a section about Hadamard matrices. That inspired me to develop a 3D model for the first 12 matrices (of edge length 2, 4, 8, 12, ... 44).

Raw data

The article https://arxiv.org/html/2411.18897v1 describes in detail how to compute the matrices with SageMath. Online you can run https://sagecell.sagemath.org/ with the following program:

from sage.combinat.matrices.hadamard_matrix import hadamard_matrix, skew_hadamard_matrix

for i in range(1,12):
  H = hadamard_matrix(4*i)
  print(i, "========")
  print(H.str())

The output can be reduced with:

perl -pe "s{\-1}{\.}g; s{[\[\]\|\+\-]}{}g; s{\A\s+\Z}{};"  infile > outfile

3D Design

Since the edge lengths increase by 4, solid blocks of bxwxh = 1x1x2 will be used to represent a one in a matrix plane, and empty space for a zero (resp. -1). The matrix planes will be stacked as a pyramid, with the 44x44 matrix at the bottom and the 4x4 at the top. Maybe the 2x2 matrix becomes the real top, maybe with blocks 1x1x1?