  A short survey on the properties of four graphs constructed in $\{0, 1\}^n$
Boolean space is presented. Flexible activation function of an artificial
neuron in a sparse distributed memory model is defined on the basis of the Ugly
duckling theorem. Cotan Laplacian on 2-face triangulation of $n$-cube has
degenerate spectrum of eigenvalues corresponding to the Hamming distance
distribution of $\{0, 1\}^n$ space. Degenerate spectrum of eigenvalues of the
cotan Laplacian defined on the graph comprising $2^n$ 2-face triangulated
$n$-cubes sharing common origin includes all integers from 0 to 3$n$, without
the eigenvalue of 3$n$-1 (multiplicities of the same eigenvalues form A038717
OEIS sequence), while the multiplicities of the same eigenvalues $[-n\sqrt{2},
n\sqrt{2}]$ of the adjacency matrix of $2^n$-cube form trinomial triangle. The
distance matrix of this graph, providing further OEIS sequences, as well as its
relation with Buckminster Fuller vector equilibrium is also discussed.
