This paper presents COSMIC (Connectivity-Oriented Sensing Method for Imaging and Communication), an innovative waveform design framework that integrates environmental radio imaging with robust communication capabilities. COSMIC introduces an extended orthogonality condition achieved through algebraic precoding across transmitting antennas, differentiating it from conventional time, frequency, or space multiplexing techniques. By leveraging the constrained imaging field of view relative to the signal duration, COSMIC enables the simultaneous transport of information while preserving high sensing performance. Numerical evaluations reveal that COSMIC significantly outperforms state-of-the-art methods, doubling the imaging Signal-to-Noise Ratio and substantially reducing the Integrated Side Lobe Ratio, thus demonstrating its effectiveness in combining communication and imaging functionalities.