A transformation T of a structure D is structure-preserving if T(D) has the same symmetry group as the original one: Aut(T(D)) ~= Aut(D).https://twitter.com/literalbanana/status/982816860566532096 …
You can add location information to your Tweets, such as your city or precise location, from the web and via third-party applications. You always have the option to delete your Tweet location history. Learn more
That is, they all break the structure in the same way: they lose symmetry across the horizontal axis, while keeping it across the vertical axis.
Why did Alexander believe there was a correct choice among the three? Perhaps as an architect, symmetry across the horizontal axis is less important, since gravity always breaks it. His preferred elaboration resembles an object standing on legs! cc: @literalbanana
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.