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Take a good look at the room and determine the best locations for the projector and screen. Check the specifications for the projector to determine the correct distance from the screen. Try to lay out the system so the projector box will screw into the ceiling joists for greater stability. If this is a new layout for the projector and screen, turn on the projector and check the image quality on the screen before attaching the mantis box to the ceiling. It's a lot easier to change the layout before the box is screwed into the ceiling.
Measure the projector and sketch out a design for the mantis box. The box should be large enough for air to circulate around the projector. Design the box as one piece; it will be cut in half later. One end of the box should be open; this is where the projector light will come out. For the top of the box (which will go against the ceiling), use horizontal wood supports instead of a solid top.
Measure and carefully cut 3/4" plywood to the dimensions in the design. Use a spade bit to cut a wide hole in one of the pieces to accommodate the projector's power cord. Always wear safety glasses and use caution when working with a power saw or any other power tools.
Assemble the box using wood glue and nails. To create a curved bottom for the box, spread glue over the edges that will attach to the bottom, then attach one end of the piece to be curved with screws. Gently bend the wood down over the box, using screws to secure. If the plywood doesn't bend over the curve easily, soak it with water before installing. Use plenty of screws to keep the top from springing out of position.