Mean ± SD, n = 50  33.2° ± 12.3°  0.9 ± 0.3 nm ± nm ± nm 0.3 ± 0.1 % B A

Figure S2. Microfibril height distribution within a lamella. A, A height image from outer onion epidermal walls. B, The height profile of the green transect in A, showing scattering of the height of microfibrils within a lamella. This result indicates that microfibrils are scattered throughout the depth of a lamella, not limited to the midpoint. 500 nm A B

Figure S3. Cell wall images from onion parenchyma (A), epidermis of Arabidopsis petioles (B), cucumber hypocotyls (C) and maize coleoptiles (D). Scale bar = 500 nm. AB C D

A B Figure S4. A pair of tilted images of HPF prepared onion epidermal walls, for 3D visualization of the sponge-like texture of the surface layer. Scale bar = 100 nm.

Figure S5. Schematic of microfibril motions in lamellae of three different orientations before (A-D) and after (A’-D’) uniaxial stretching. A: relaxed wall with three stacked lamella, B-D: individual lamellae with distinctive cellulose orientations; A’-D’ unilaterally stretched wall, showing microfibril slippage and closer packing of microfibrils in lamella B, increased spread between microfibrils which are forced into greater bending due to lateral shrinkage in lamella C, and a combination of slippage, axial reorientation and lateral compression in lamella D. Note the three distinctive patterns of motion: (1) In lamellae with microfibrils parallel to the stretch direction, microfibrils undergo straightening and sliding relative to one another, accompanied by a reduction in the space between microfibrils. This follows from the facts that the very high modulus of cellulose microfibrils limits elastic extension to <5% (Wu et al. 2014) and that microfibril straightening can account for only part of the lamellar extension. (2) In lamellae at right angles to the stretch, the lateral spacing between microfibrils must increase, potentially restricted at sites of microfibril bundling, and microfibril curvature may increase, partly due to in-plane distortion of the reticulated network of microfibrils and partly due to the out-of-plane wrinkling of the cell wall. (3) In lamellae with microfibrils oriented ~30-60 o to the direction of stretch, microfibrils will passively reorient in the stretch direction, and lateral spacing will also be reduced. A A’ B’ C’ D’ B C D