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Abstract An elastic map $\mathbf {T}$ T describes the strainstress relation at a particular point $\mathbf {p}$ p in some material. A symmetry of $\mathbf {T}$ T is a rotation of the material, about $\mathbf {p}$ p , that does not change $\mathbf {T}$ T . We describe two ways of inferring the group $\mathcal {S} _{ \mathbf {T} }$ S T of symmetries of any elastic map $\mathbf {T}$ T ; one way is qualitative and visual, the other is quantitative. In the first method, we associate to each $\mathbf {T}$ T its “monoclinic distance function” "Equation missing" on the unit sphere. The function "Equation missing" is invariant under all of the symmetries of $\mathbf {T}$ T , so the group $\mathcal {S} _{ \mathbf {T} }$ S T is seen, approximately, in a contour plot of "Equation missing" . The second method is harder to summarize, but it complements the first by providing an algorithm to compute the symmetry group $\mathcal {S} _{ \mathbf {T} }$ S T . In addition to $\mathcal {S} _{ \mathbf {T} }$ S T , the algorithm gives a quantitative description of the overall approximate symmetry of $\mathbf {T}$ T . Mathematica codes are provided for implementing both the visual and the quantitative approaches.more » « less

null (Ed.)The elastic map, or generalized Hooke’s Law, associates stress with strain in an elastic material. A symmetry of the elastic map is a reorientation of the material that does not change the map. We treat the topic of elastic symmetry conceptually and pictorially. The elastic map is assumed to be linear, and we study it using standard notions from linear algebra—not tensor algebra. We depict strain and stress using the “beachballs” familiar to seismologists. The elastic map, whose inputs and outputs are strains and stresses, is in turn depicted using beachballs. We are able to infer the symmetries for most elastic maps, sometimes just by inspection of their beachball depictions. Many of our results will be familiar, but our versions are simpler and more transparent than their counterparts in the literature.more » « less