  We study the problem of determining the least symmetric triangle, which
arises both from pure geometry and from the study of molecular chirality in
chemistry. Using the correspondence between planar $n$-gons and points in the
Grassmannian of 2-planes in real $n$-space introduced by Hausmann and Knutson,
this corresponds to finding the point in the fundamental domain of the
hyperoctahedral group action on the Grassmannian which is furthest from the
boundary, which we compute exactly. We also determine the least symmetric
obtuse and acute triangles. These calculations provide prototypes for
computations on polygon and shape spaces.
