Abstract. A t-regular graph of radius s is radial Moore if it has diameter s+1 and

Ms,t=1+t+(t-1)t+(t-1)t2+...+(t-1)ts-1

vertices. We construct radial Moore graphs of radius 3 and degrees t=3,5,7,9,10,11,...,30 with at least t+1 central vertices and at most t+2 orbits under the automorphism group. Together with our previous result and with a nice result of Exoo, Gimbert, Lopez and Gomez, we now get that for every t≥3there exists a radial Moore graph of radius 3 and degree t.