  We introduce a minimal model describing the physics of classical
two-dimensional (2D) frustrated Heisenberg systems, where spins order in a
non-planar way at T=0. This model, consisting of coupled trihedra (or
Ising-$\mathbb{R}P^3$ model), encompasses Ising (chiral) degrees of freedom,
spin-wave excitations and $\Z_2$ vortices. Extensive Monte Carlo simulations
show that the T=0 chiral order disappears at finite temperature in a continuous
phase transition in the 2D Ising universality class, despite misleading
intermediate-size effects observed at the transition. The analysis of
configurations reveals that short-range spin fluctuations and $\Z_2$ vortices
proliferate near the chiral domain walls explaining the strong renormalization
of the transition temperature. Chiral domain walls can themselves carry an
unlocalized $\Z_2$ topological charge, and vortices are then preferentially
paired with charged walls. Further, we conjecture that the anomalous
size-effects suggest the proximity of the present model to a tricritical point.
A body of results is presented, that all support this claim: (i) First-order
transitions obtained by Monte Carlo simulations on several related models (ii)
Approximate mapping between the Ising-$\mathbb{R}P^3$ model and a dilute Ising
model (exhibiting a tricritical point) and, finally, (iii) Mean-field results
obtained for Ising-multispin Hamiltonians, derived from the high-temperature
expansion for the vector spins of the Ising-$\mathbb{R}P^3$ model.
