The Collaborative International Dictionary of English v.0.48:

Trapezohedron \Trap`e*zo*he"dron\, n. [NL., from trapezium + Gr.
   ? seat, base, fr. ? to sit.] (Crystalloq.)
   (a) A solid bounded by twenty-four equal and similar
       trapeziums; a tetragonal trisoctahedron. See the Note
       under Trisoctahedron.
   (b) A tetartohedral solid of the hexagonal system, bounded by
       six trapezoidal planes. The faces of this form are common
       on quartz crystals.
       [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

WordNet (r) 3.0 (2006):

trapezohedron
    n 1: a polyhedron whose faces are trapeziums