An X-ray detector is formed with a geometry in the form of a spherical polygon, including an entrance window, a grid and an anode. The spherical polygonal entrance window and the grid form a spherical polygonal drift region between them. The electric field in this region is radial and eliminates parallax broadening. A spherical polygonal amplification region between a resistive anode on an insulating support and the grid allows very high gas amplification and good protection against spark discharges. A readout electrode on the back side of the anode insulator detects induced charges and protects the readout electronics against sparks.