The Collaborative International Dictionary of English v.0.48:

Trisoctahedron \Tris*oc`ta*he"dron\, n. [Gr. ? thrice + FE.
   octahedron.] (Crystallog.)
   A solid of the isometric system bounded by twenty-four equal
   faces, three corresponding to each face of an octahedron.
   [1913 Webster]

   Tetragonal trisoctahedron, a trisoctahedron each face of
      which is a quadrilateral; called also trapezohedron and
      icositetrahedron.

   Trigonal trisoctahedron, a trisoctahedron each face of
      which is an isosceles triangle.
      [1913 Webster] Trispast