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]