V+F-E=2 (number of vertices v, number of faces f, number of edges e)

Then it is proved that all faces of a simple polyhedron are triangles, and it is proved that the number of vertices v and the number of faces f have the following relationship: f = 2v-4.

Proof: ∫E = 3F/2, v+f-e = 2.

∴V+F-3F/2=2,∴F=2V-4

Therefore, the convex polygon formed when the hedgehog becomes a ball can be transformed into as many faces as there are different ways to support the body. Moreover, any three adjacent thorns in the topic can support the body, and any four thorns can know that every face of this polygon must be a triangle.

Because hedgehog has 2006 spines, which is equivalent to 2006 vertices, substitute the formula F = 2v-4 proved above into V=2006, and get F=4008, so the answer is A.