If the ramp could be made from a plane, its boundaries would be parallel spirals, that is, they have the same center and rate of growth. I'm not sure the ramp can be made from a flat sheet of paper though. I am assuming the distance between two points on the flat surface will equal the length of the geodesic between the transformed points. I am not sure this is true but the pieces seem to work in the cardboard model. There is more.
Tessellation Strictly speaking tessellations are tiles that cover the plane without gaps or overlap.
I extend this idea into three dimensions though. I also label tesselations polyhedra that stack to fill space without gaps or overlap. Tessellations, My Blocks Vs Zaks Toys that tessellate have the power to approximate any shape. This page discusses this power and also contrasts my block with a similar toy that does not tessellate as well as Delta Blocks. This page discusses my toy which was inspired by M.C. Escher's print Flatworms.