Both 1D physics (dimensional frustration) and geometric frustration offer ways of achieving unusual quantum ground states that defy the usual tendency for systems to order at low temperature. The third law of thermodynamics however imposes that the system must find a single ground state. Real materials often wriggle out of facing this dilemma. 1D materials may undergo a type of distortion known as a Peierls transition due to an interaction with the lattice, while long range interactions may circumvent geometric frustration. In this experiment we will determine the magnetic structure of a material that has both sources of frustration, each acting to eliminate the wriggle room of the other. A truly frustrated ground state could have quantum correlations that extend over long distances that are useful for making novel quantum devices.