Christoph's Jewel was designed by Christoph Bandelow. It is now being produced by Meffert. It is equivalent to a Corner-Turning Octahedron without the tips.
Corner-turning octahedrons are themselves equivalent to a 3x3x3 cube with no corners and with the centre pieces marked to show orientation. The first two layers solve simply using Pyraminx type moves. The last layer needs edges oriented and permuted. Sometimes the centre has to be rotated too.