The centroid is the only affine equivariant center of a triangle, but more general convex bodies can have other affine equivariant centers; see e.g. Neumann, B. H. (1939), "On some affine invariants of closed convex regions", Journal of the London Mathematical Society, Second Series, 14 (4): 262–272, doi:10.1112/jlms/s1-14.4.262, MR0000978.
Segal, G. B. (1971), "Equivariant stable homotopy theory", Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 2, Gauthier-Villars, Paris, pp. 59–63, MR0423340.
The centroid is the only affine equivariant center of a triangle, but more general convex bodies can have other affine equivariant centers; see e.g. Neumann, B. H. (1939), "On some affine invariants of closed convex regions", Journal of the London Mathematical Society, Second Series, 14 (4): 262–272, doi:10.1112/jlms/s1-14.4.262, MR0000978.
Sarle, Warren S. (September 14, 1997), Measurement theory: Frequently asked questions (Version 3)(PDF), SAS Institute Inc.. Revision of a chapter in Disseminations of the International Statistical Applications Institute (4th ed.), vol. 1, 1995, Wichita: ACG Press, pp. 61–66.