Thesis

The number of facets forming an intersection of n cylinders is

F(n) = n*(n-1)*2

Prove by induction

F(1)=1

F(2)=4

Remember

the Sum i=1 to n of i is n*(n+1)/2

hence

F(n) = n*(n-1)*2

= 4* (Sum i=1 to n-1 of i)

= 4* (Sum i=1 to n-2 of i) + 4*(n-1)

= F(n-1) + 4*(n-1)

The n th cylinder forms 4 new facets with each of the already present n-1 cylinders. He hits the other cylinder at two opponent places and splits there for two different directions one facet in two.

P.S.

Often the situation is degenerateted and very small facets are even vanishing so that F(n) gives an upper limit for the number of facets.

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