The Collaborative International Dictionary of English v.0.48:

Icositetrahedron \I`co*si*tet`ra*he"dron\, n. [Gr. ? twenty + ?,
   combining form of ? four + ? seat, base.] (Crystallog.)
   A twenty-four-sided solid; a tetragonal trisoctahedron or
   trapezohedron.
   [1913 Webster]

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