The following wiring diagram is how I recently re-wired the switches for the vacuum system at my business (even though I used a light as the load for this diagram). As a 4-way switch naturally crosses the circuit (bottom right to top left and bottom left to top right), I thought it best to connect the red and black traveler wires using this same cross-over pattern which represents how the switch connects and disconnects the circuit. This works as long as both 3-way switches are wired exactly the same as each other. If the 3-way switches are not wired the same (red and black reversed), then the 4-way switch would need to have both red wires on one side and both black wires on the other – not in the natural crossover pattern shown here. I could not find anywhere on the internet a diagram like the one I have provided below, so I just made my own. I hope this helps.
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The Professor Twist Files 