  We employ spherical $t$-designs for the systematic construction of solids
whose rotational degrees of freedom can be made robust to decoherence due to
external fluctuating fields while simultaneously retaining their sensitivity to
signals of interest. Specifically, the ratio of signal phase accumulation rate
from a nearby source to the decoherence rate caused by fluctuating fields from
more distant sources can be incremented to any desired level by using
increasingly complex shapes. This allows for the generation of long-lived
macroscopic quantum superpositions of rotational degrees of freedom and the
robust generation of entanglement between two or more such solids with
applications in robust quantum sensing and precision metrology as well as
quantum registers.
