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The organization of micron-sized, multi-microtubule arrays from individual microtubules is essential for diverse cellular functions. The microtubule polymer is largely viewed as a passive building block during the organization process. An exception is the ‘tubulin code’ where alterations to tubulin at the amino acid level can influence the activity of microtubule-associated proteins. Recent studies reveal that micron-scale geometrical features of individual microtubules and polymer networks, such as microtubule length, overlap length, contact angle, and lattice defects, can also regulate the activity of microtubule-associated proteins and modulate polymer dynamics. We discuss how the interplay between such geometrical properties of the microtubule lattice and the activity of associated proteins direct multiple aspects of array organization, from microtubule nucleation and coalignment to specification of array dimensions and remodeling of dynamic networks. The mechanisms reviewed here highlight micron-sized features of microtubules as critical parameters to be routinely investigated in the study of microtubule self-organization.