The rapid evolution of multi-display environments (MDEs) has created a vacuum in need of novel input devices to optimize interaction in MDEs. In this paper, we propose TDome, a novel touch-enabled 6DOF input and output device to facilitate interactions in MDEs. TDome offers a private display as output, and multiple degrees of freedom as input by combining touch gestures on the display with physical rotation, roll and translation manipulations of the device. TDome allows versatile interactions that address major MDE tasks, which we illustrate through various proof-of-concept implementations: detect surrounding displays, select one display, transfer data across displays, reach distant displays and perform private interactions. We explore TDome's usability and suitability for MDEs through three user studies. First we explore combined physical+touch gestures from which we discard uncomfortable combinations. We experimentally validate their feasibility and come up with a set of 71 combined gestures that can be easily performed and efficiently detected. Finally, we collect user feedback to identify natural mappings between gestures and MDE interactions.