ping the public IP from where?
the public IP is supposed to be on separate network than the mgmt IPs... The public IP should be reachable from "outside" ie whereever you want to access your OpenStack cloud/Horizon dashboard from.
Are you able to login to Horizon dashboard?
The IP is supposed to be on a different network. I have another VM which is on the other network from which I am trying to access the horizon dashboard. I am able to bring up the dashboard through the controller IP address from which the login is not allowed. I am running with the VDS configuration.