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Cut 2 pieces of cardboard into circles that are 3 1/2" in diameter. Hot glue them together to make them stronger, avoiding the center for when you drill later. Measure and draw 2 perpendicular lines intersecting in the center. Drill through that center mark with a piece of wood behind the cardboard for safety.
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Paint the front and sides of your clock face. While that dries, sand, cut and spray paint 12 13" dowels.
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On the back of your clock face, draw 6 equidistant lines intersecting in the center as your guide.
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Cut away any excess material around the center hole with a utility knife so the clock can fit.
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Align both 12 o'clocks on your clock and grid before gluing the two pieces together. Be careful not to get any hot glue on the center piece.
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Add your clock hands and the top small screw to the face.
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Using the grid as your guide, hot glue your dowels onto the back of the clock. Using a roll of tape can stabilize the surface area for this step. A bird's eye view can help you see if the dowels align.
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Add a screw to the perfect spot and hang your atomic age clock.