The hyper hexa-cell (HHC) interconnection network is relatively a new interconnection network, which is constructed from hexa-cell and hypercube topologies. HHC is developed to support parallel algorithms for solving computation and communication intensive problems. Thus, in order to support solving these problems efficiently, this paper presents two broadcast communication operations for HHC using store-and-forward technique; namely, one-to-all and all-to-all broadcast operations; which allow a message to be transmitted through the shortest path from the source node to all other nodes. The broadcast communication operations are evaluated analytically in terms of communication steps, communication latency, communication cost, and speed over HHC and wraparound square mesh interconnection networks. The analytical results over HHC show that in both one-to-all and all-to-all broadcast operations, the maximum communication steps are , where d is the dimension of HHC, which is a small integer number. Also, the communication latency increases linearly when the network size increases, and the communication cost for the broadcast operations is equal to O(. Moreover, the speed of both broadcast operations on d-dimensional HHC is speed of electronic links. In comparison between HHC and wraparound square mesh, one-to-all and all-to-all broadcast communication operations over HHC perform much better than mesh in terms of maximum communication steps, communication latency, and speed.