Geiger-mode avalanche photodiodes (G-APD, SiPM) are a much discussed alternative to photomultiplier tubes in Cherenkov astronomy. The First G-APD Cherenkov Telescope (FACT) collaboration builds a camera based on a hexagonal array of 1440 G-APDs and has now finalized its construction phase. A light-collecting solid PMMA cone is glued to each G-APD to eliminate dead space between the G-APDs by increasing the active area, and to restrict the light collection angle of the sensor to the reflector area in order to reduce the amount of background light. The processing of the signals is integrated in the camera and includes the digitization using the domino ring sampling chip DRS4. (C) 2011 Elsevier B.V. All rights reserved.