We propose, analyze and offer sample designs and results for a high-flux photovoltaic concentrator comprised of a large-aperture paraboloidal-dish primary concentrator, and a second-stage kaleidoscope flux homogenizer. The following key design aims are all satisfied: (1) highly uniform irradiance on the solar cell absorber; (2) maximum collection efficiency; and (3) not exceeding the prescribed target flux level (for illustrative purposes here taken to be 500 suns), despite the dish being capable of much higher concentration. As a result of recent advances in the low cost and ease of production of large dish concentrators, the kaleidoscope-based design offers an intriguing alternative to other high-concentration optical designs developed to date. Admissible kaleidoscope geometries are identified. We generate quantitative results for a compact practical design that incurs low optical losses, and produces a highly homogeneous flux map.