  A study of fermion nodes for spin-polarized states of a few-electron ions and
molecules with $s,p,d$ one-particle orbitals is presented. We find exact nodes
for some cases of two electron atomic and molecular states and also the first
exact node for the three-electron atomic system in $^4S(p^3)$ state using
appropriate coordinate maps and wavefunction symmetries. We analyze the cases
of nodes for larger number of electrons in the Hartree-Fock approximation and
for some cases we find transformations for projecting the high-dimensional node
manifolds into 3D space. The node topologies and other properties are studied
using these projections. We also propose a general coordinate transformation as
an extension of Feynman-Cohen backflow coordinates to both simplify the nodal
description and as a new variational freedom for quantum Monte Carlo trial
wavefunctions.
