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We report density functional theory calculations for Mo$_3$S$_7$(dmit)$_3$.We derive an ab initio tight-binding model from overlaps of Wannier orbitals;finding a layered model with interlayer hopping terms $\sim3/4$ the size of thein-plane terms. The in-plane Hamiltonian interpolates the kagom\'e andhoneycomb lattices. It supports states localized to dodecahedral rings withinthe plane, which populate one-dimensional (1D) bands and lead to a quasi-1Dspin-one model on a layered honeycomb lattice once interactions are included.Two lines of Dirac cones also cross the Fermi energy.

Emergence of quasi-one-dimensional physics in Mo$_3$S$_7$(dmit)$_3$, a nearly-isotropic three-dimensional molecular crystal