Figure 1.

Thermal mechanisms a bi-material tetrahedron featuring either a stationary-node (a-I) or stationary-lines (b-I). II and III show visually uncoupled thermal expansions, one for the low-CTE material and the other for the high-CTE material; IV shows the overall thermal expansion of the tetrahedron. Application of bi-material tetrahedra to the Octet cells (c,f). (c) Iso-CTE Octet obtained by assembling 8 stationary-node tetrahedra with skew angle (θ_I) of 60° and 50° on a regular octahedron (red core). (d,e) isotropic CTE properties plotted in polar and spherical coordinates. (f) Aniso-CTE Octet (skew angle θ_A = 60°) with directional CTE obtained with stationary-lines tetrahedra. (g,h) anisotropic CTE properties with low CTE in the z-direction. The green dashed line in (d,g) represents points with zero thermal expansion (Supplementary Information–Video 1).