  Bounded domains have discrete eigenfrequencies/spectra, and cavities with
different boundaries and areas have different spectra. A general methodology
for isospectral twinning, whereby the spectra of different cavities are made to
coincide, is created by combining ideas from across physics including
transformation optics, inverse problems and metamaterial cloaking. We twin a
hexagonal drum with a deformed hexagonal drum using a non-singular coordinate
transform that adjusts the deformed shape by mapping a near boundary domain to
a zone of heterogeneous anisotropic medium. Splines define the mapping zone for
twinning these two drums and we verify isospectrality by finite element
analysis.
