  We consider the transverse field Ising model in $(2+1)$D, putting 12 spins at
the vertices of the regular icosahedron. The model is tiny by the exact
diagonalization standards, and breaks rotation invariance. Yet we show that it
allows a meaningful comparison to the 3D Ising CFT on $\mathbb{R}\times S^2$,
by including effective perturbations of the CFT Hamiltonian with a handful of
local operators. This extreme example shows the power of conformal perturbation
theory in understanding finite $N$ effects in models on regularized $S^2$. Its
ideal arena of application should be the recently proposed models of fuzzy
sphere regularization.
