Sticky-ended DNA duplexes can associate spontaneously into long double helices; however, such self-assembly is much less developed with proteins. Collagen is the most prevalent component of the extracellular matrix and a common clinical biomaterial. As for natural DNA, the ~103-residue triple helices (~300 nm) of natural collagen are recalcitrant to chemical synthesis. Here we show how the self-assembly of short collagen-mimetic peptides (CMPs) can enable the fabrication of synthetic collagen triple helices that are nearly a micrometre in length. Inspired by the mathematics of tessellations, we derive rules for the design of single CMPs that self-assemble into long triple helices with perfect symmetry. Sticky ends thus created are uniform across the assembly and drive its growth. Enacting this design yields individual triple helices that, in length, match or exceed those in natural collagen and are remarkably thermostable, despite the absence of higher-order association. The symmetric assembly of CMPs provides an enabling platform for the development of advanced materials for medicine and nanotechnology.