  We present quantum simulation experiments of Ising-like spins on Platonic
graphs, which are performed with two-dimensional arrays of Rydberg atoms and
quantum-wire couplings. The quantum wires are used to couple otherwise
uncoupled long-distance atoms, enabling topology-preserving transformtions of
the three-dimensional graphs to the two-dimensional plane. We implement three
Platonic graphs, tetrahedron, cube, and octahedron of Platonic solids, and
successfully probe their ground many-body spin configurations before and after
the quasi-adiabatic control of the system Hamiltonians from the paramagnetic
phase to anti-ferromagnetic-like phases. Our small-scale quantum simulations of
using less than 22 atoms are limited by experimental imperfections, which can
be easily improved by the state-of-the-art Rydberg-atom technologies for more
than 1000-atom scales. Our quantum-wire approach is expected to pave a new
route towards large-scale quantum simulations.
