Walks, Paths and Connectivity · Hard problem

Three triangles are arranged in a ring: triangle $1,2,3$, triangle $4,5,6$, and triangle $7,8,9$, connected by the three edges $34$, $67$, and $91$, which close the chain back into a loop (edges $12,23,31,45,56,64,78,89,97,34,67,91$). How many cut vertices does this graph have?