An elastic map $\mathbf{T}$
T
associates stress with strain in some material. A symmetry of $\mathbf{T}$
T
is a rotation of the material that leaves $\mathbf{T}$
T
unchanged, and the symmetry group of $\mathbf{T}$
T
consists of all such rotations. The symmetry class of $\mathbf{T}$
T
describes the symmetry group but without the orientation information. With an eye toward geophysical applications, Browaeys & Chevrot developed a theory which, for any elastic map $\mathbf{T}$
T
and for each of six symmetry classes $\Sigma $
Σ
, computes the “$\Sigma $
Σ
-percentage” of $\mathbf{T}$
T
. The theory also finds a “hexagonal approximation”—an approximation to $\mathbf{T}$
T
whose symmetry class is at least transverse isotropic. We reexamine their theory and recommend that the $\Sigma $
Σ
-percentages be abandoned. We also recommend that the hexagonal approximations to $\mathbf{T}$
T
be replaced with the closest transverse isotropic maps to $\mathbf{T}$
T
.