Carbon nanotubes of uniform size may soon be available in macroscopic quantities. Here we examine the ordered condensed phase of these tubes. As the tube diameter varies, the structural properties show a clear transition between two regimes with qualitatively different behavior. Tubes 10 \AA{} and less in diameter behave as rigid cylinders. For diameters over 25 \AA{}, the tubes flatten against each other under the van der Waals attraction, forming a honeycomb structure. This structure exhibits an anomalous rigidity, which does not decrease as expected with increasing tube diameter. Based on reported tube sizes, both regimes should be experimentally accessible.