Fig. 3. Symmetry in the yarn segments between stitches.

Two similar stitches (K-K or P-P) are joined by a yarn segment with even symmetry, highlighted in pink (a top). Extensional deformations cause curvature deformations of the yarn segment (a bottom). Alternating stitches (K-P) are joined by a yarn segment with odd symmetry, highlighted in cyan (b top). These segments are able to rotate to accommodate extensional deformation (b bottom). Symmetries of stitches are shown in the x-direction (c–f) and the y-direction (g–j). c, g Stockinette fabric has only even connecting yarn segments in both x- (c) and y-directions (g). d, h Garter fabric has even connecting yarn segments in x-direction (d) and odd connecting yarn segments in the y-direction (h). e, i Rib fabric has odd connecting yarn segments in the x-direction (e) and even connecting yarn segments in the y-direction (i). f, j Since seed fabric is based on a checkerboard pattern, it only has odd connecting yarn segments. The renderings in (a-j) are repeated unit cells of sample stitch-level simulation outputs. A comparison of Young’s moduli measured in experimental samples $Y^{\exp }$ with those computed in the reduced-symmetry (RS) model Y^RS (Supplementary Tables 17, 18) is shown in (k). Dark and light symbols indicate extensional rigidity in the x-direction and y-direction, respectively, filled symbols indicate acrylic yarn, and open symbols indicate cotton yarn. This demonstrates that our simple composite model has both qualitative and quantitative agreement with our experimental measurements. Source data are provided as a Source Data file.