Let (2,2,2,2) be ramification indices for the Riemann sphere. It is well known that the regular branched covering map corresponding to this, is the Weierstrass P function. Lattes  gives a rational function R(z)=
which is chaotic on
and is induced by the Weierstrass P function and the linear map L(z) = 2z on complex plane C. It is also known that there exist regular branched covering maps from
if and only if the ramification indices are (2,2,2,2), (2,4,4), (2,3,6) and (3,3,3), by the Riemann-Hurwitz formula. In this paper we will construct regular branched covering maps corresponding to the ramification indices (2,4,4), (2,3,6) and (3,3,3), as well as chaotic maps induced by these regular branched covering maps.