This paper presents the design and implementation of Geosphere, a physical- and link-layer design for access point-based MIMO wireless networks that consistently improves network throughput. To send multiple streams of data in a MIMO system, prior designs rely on a technique called zero-forcing, a way of "nulling" the interference between data streams by mathematically inverting the wireless channel matrix. In general, zero-forcing is highly effective, significantly improving throughput. But in certain physical situations, the MIMO channel matrix can become "poorly conditioned," harming performance. With these situations in mind, Geosphere uses sphere decoding, a more computationally demanding technique that can achieve higher throughput in such channels. To overcome the sphere decoder's computational complexity when sending dense wireless constellations at a high rate, Geosphere introduces search and pruning techniques that incorporate novel geometric reasoning about the wireless constellation. These techniques reduce computational complexity of 256-QAM systems by almost one order of magnitude, bringing computational demands in line with current 16- and 64-QAM systems already realized in ASIC. Geosphere thus makes the sphere decoder practical for the first time in a 4 x 4 MIMO, 256-QAM system. Results from our WARP testbed show that Geosphere achieves throughput gains over multi-user MIMO of 2x in 4 x 4 systems and 47% in 2 x 2 MIMO systems.