Terrestrial wireless sensor networks are generally designed based on the assumption that sensor nodes are deployed on a two-dimensional (2D) plane. This assumption is usually invalid in an underwater sensor network, where sensor nodes may be deployed at various depths, thus creating a three-dimensional (3D) network. Other important applications of 3D networks also include future space and atmospheric networks. Consequently, new research challenges now exist in the field of wireless sensor networks, as several coverage and connectivity issues unique to 3D networks require resolution. For example, node placement strategies need to deploy the minimum number of sensor nodes and, at the same time, ensure that all points inside the network are within the sensing range of at least one sensor. All sensor nodes also need to communicate with each other, possibly over a multi-hop path. Establishment of this type of network will depend on the ratio of the communication range and the sensing range of each sensor. In this study, we use deterministic homogeneous sphere based communication and sensing range model to solve this issue, by placing a node at the center of each virtual cell created by truncated octahedron based tessellation of 3D space. This works well when the ratio of communication range and sensing range is greater than 1.7889. On the other hand, for smaller values of this ratio, the solution depends on the degree of communication redundancy needed by the network. We provide solutions for both limited and full communication redundancy requirements. We also investigate coverage and connectivity issues in 3D networks where nodes were randomly deployed. Since node location can be random, redundant nodes have to be deployed to achieve 100% sensing coverage. However, at any particular time, not all nodes are needed to achieve full sensing coverage. Consequently, a subset of sensor nodes can be dynamically chosen to remain active at a given time to achieve sensing coverage based on their location at that time. One approach to achieve that goal in a distributed and scalable way is to partition the 3D network space into virtual regions or cells, and to keep one node active in each cell. Following this approach, we achieve a fully distributed and highly scalable solution that minimizes the number of active nodes that use cells created by truncated octahedral tessellation of 3D space. By adjusting the radius of each cell, this scheme can be used to achieve k-coverage where a point inside a network has to be within the sensing of k different sensor nodes with high probability. We analyze the performance of this scheme and found that performance improves significantly where value of k is larger than 1.