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Adjacency matrices of the first five hemi-hypercubes

White fields are 0s. Orange and red entries are 1s.
These graphs are undirected, therefore each edge is represented by two entries, which are symmetric to the main diagonal.

The 4×4 matrix with 8 + 4 = 12 entries represents the hemi-cube, which has 4 vertices and six edges.
The 8×8 matrix with 24 + 8 = 32 entries represents the hemi-tesseract, which has 8 vertices and 16 edges.

They are adjacency matrices of the next smaller hypercube (compare this adjacency matrix of the 8-cube) together with the antidiagonal,

which means that each hemi-hypercube is the hypercube of the lower dimension, with additional edges between all complements.
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