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The Collaborative International Dictionary of English v.0.48:

Halfpace \Half"pace`\ (-p[=a]s`), n. (Arch.) A platform of a staircase where the stair turns back in exactly the reverse direction of the lower flight. See Quarterpace. [1913 Webster] Note: This term and quarterpace are rare or unknown in the United States, platform or landing being used instead. [1913 Webster]