Source : Webster's Revised Unabridged Dictionary (1913)

Halfpace \Half"pace`\, n. (Arch.)
   A platform of a staircase where the stair turns back in
   exactly the reverse direction of the lower flight. See
   {Quarterpace}.

   Note: This term and quartepace are rare or unknown in the
         United States, {platform} or {landing} being used
         instead.