What molecular conformation (structure) of homologous chromosomes facilitates crossing over?

tetrad

meiosis II

triads

mitosis

The molecular conformation that facilitates crossing over is: tetrad.

Homologous chromosomes form tetrads composed of four sister chromatids. These chromatids are then able to cross over.

This happens during the stage of Meiosis I - in Meiosis II the tetrad has already split into pairs of sister chromatids.