  The symmetry of the whole experimental setups, including specific sample
environments and measurables, can be compared with that of specimens for
observable physical phenomena. We, first, focus on one-dimensional (1D)
experimental setups, independent from any spatial rotation around one
direction, and show that eight kinds of 1D objects (four; vectorlike, the other
four; director-like), defined in terms of symmetry, and their dot and cross
products are an effective way for the symmetry consideration. The dot products
form a Z2xZ2xZ2 group with Abelian additive operation, and the cross products
form a Z2xZ2 group with Abelian additive operation or Q8, a non-abelian group
of order eight, depending on their signs. Those 1D objects are associated with
characteristic physical phenomena. When a 3D specimen has Symmetry Operational
Similarity (SOS) with (identical or lower, but not higher, symmetries than) an
1D object with a particular phenomenon, the 3D specimen can exhibit the
phenomenon. This SOS approach can be a transformative and unconventional avenue
for symmetry-guided materials designs and discoveries.
