Raspberry Pi video players
The prototype hardware
Dimensions: 40.5 x 19 x 17 cm.

The lower part of the box just holds a mains distribution block, the power supplies for the Raspberry Pis and the ethernet switch, and surplus power and ethernet cable.
The unit could be made more compact by using one power supply for the computers and the switch, but this would have to be carefully specified because the Raspberry Pi is quite sensitive to power quality.
The top half could be completely open if the computers were securely fastened so that the HDMI cables could be inserted and removed easily.
All access to the filestores is via FTP and SSH so there is no real need to remove the SD cards.