Radically novel materials, liquid crystalline elastomers and glasses, change shape by 100s% following changes in temperature or illumination. Shape change, that is elongation along a particular direction, rather than simply change of volume, can be imaginatively arranged induce intrinsic curvature in initially ­ at spaces. The intimate connection between di‑ erential geometry and mechanics comes into play and suggests ways of exploiting light-induced curvature of space for new mechanics paradigms. I will give, with many demonstrations, examples of the geometry arising. These solids can apparently solve the map-maker’s problem of resolving planes with curved space. I will say how this unique property might be exploited in strong actuation.