This is a similar case to that of dead, live and revolving centres where misconceptions of the correct name propagates and is now appearing incorrectly in lathe manuals.
A spider is the device, 3 or 4 screws at the rear end of a mandrel to centralise and steady long stock. It has a number of thin screw sticking out so if detached and left in the tool box the analogy is obvious. Only a nit picking arachnologist is going to care about the number of legs. The one linked by MG above is not a spider, just a good idea needing a better name than 'spacer' but shouldn't nick something else's name.
well I'm blowed a little red arachnid has chosen this moment to crawl across my laptop screen.