TITLE: Is there a 2-connected k-regular graph without Hamiltonian path?
QUESTION [12 upvotes]: In this paper (Construction 2.6 p860) the authors have built examples of 
connected $k$-regular graph without Hamiltonian path, but with a cut-vertex (i.e. it is not $2$-connected). 
Question: Is there a $2$-connected $k$-regular graph without Hamiltonian path?
Remark: every $2$-connected $k$-regular graph with at most $3k+3$ vertices admits a Hamiltonian cycle or is one of the two exceptions, which admit a Hamiltonian path.

REPLY [4 votes]: The smallest graph coming from the construction of Fedor Petrov's answer can be realized as follows: