7 Arm Sphidron

Spidrons were invented by Daniel Erdely in 1979 as a homework assignment for Erno Rubik, inventor of the Rubik's Cube. Spidrons can folded into expandable 3D shapes and can be applied to polyhedrons and tessellations. The original spidron can form a tiling with 3 spiral arms. Sphidrons are similar to spidrons except they are smooth. Now, here is the big question: is it possible to "roll" a single piece of paper into a shape that looks something like this, without stretching the paper?