Do you mean to say there will not be any access to Wi-Fi network where the three photons will be located? Photon comes with Wi-Fi access by default, but there must be a network available to connect to the cloud.
Your phone was used to connect the photon to the an existing Wi-FI network by providing the SSID and the password. It did not create a network.
I believe you are talking about one of the photons being an Access Point (AP) and the photons talking to each other using this access point. As per the discussion in the comunioty form, this feature is being added. @mdma can provide an update on this.
Do you want to consider wireless protocols such as Zigbee or Bluetooth for the photons to communicate with each other? These can be used for short distance communication.