The triangles in your reference image are not equilateral, they’re close, but you cannot create a freeform shape using equilateral triangles.
Each triangle must have the same edge lengths as all its neighbours, otherwise there would be gaps in the surface. Furthermore all three edges of each triangle must have the same length, otherwise they would not be equilateral. So all the triangles in your entire mesh are identical.
The only curvature possible under such constraints is one where you fold the shape along a set of edges that are all colinear and touch the boundary of the shape at both ends, or when you create a different topology where fewer or more than 6 triangles meet in some vertices.