KURSCHAK 1984 Problem 2

$A_1B_1A_2$ , $B_1A_2B_2$ , $A_2B_2A_3$ ,..., $B_{13}A_{14}B_{14}$ , $A_{14}B_{14}A_1$ and $B_{14}A_1B_1$ are equilateral rigid plates that can be folded along the edges $A_1B_1$ , $B_1A_2$ , ..., $A_{14}B_{14}$ and $B_{14}A_1$ respectively. Can they be folded so that all $28$ plates lie in the same plane?