trapezohedron

From trapezium +‎ -hedron, with trapezium used in the US sense of a convex irregular quadrilateral.

trapezohedron (plural trapezohedra or trapezohedrons)

1. (geometry, crystallography) Any of a class of polyhedra that have kite-shaped faces and are dual polyhedra of antiprisms.
   • 1969, Carl W. Correns, William D. Johns (translator), Introduction to Mineralogy: Crystallography and Petrology, 2nd Edition, page 40,

     The general form is called the tetragonal trapezohedron. In this case also there are both left- (Fig. 97) and right-handed (Fig. 98) forms.

   • 2002, John Montroll, A Plethora of Polyhedra in Origami‎, page 105:

     This trapezohedron, or antidiamond, is composed of ten quadrilaterals. In each quadrilateral, three of the angles are 108° and one is 36°.

2. (crystallography) A deltoidal icositetrahedron.
   • 1998, Cornelius S. Hurlbut Jr., W. Edwin Sharp, Dana's Minerals and How to Study Them (After Edward Salisbury Dana), page 23,

     A trapezohedron has 24 equal faces, each a four-sided figure or trapezium. Unlike the forms already described, which are always the same, there are several different trapezohedrons, all having the same number of faces but differing in the angles between the faces.

In crystallography, trapezohedron usually refers to the second (deltoidal icositetrahedron) sense, although crystals exist in both shapes.

• (polyhedron whose faces are kites): antibipyramid, antidipyramid, deltohedron
• (deltoidal icositetrahedron): deltoidal icositetrahedron, strombic icositetrahedron, tetragonal icosikaitetrahedron, tetragonal trisoctahedron, trapezoidal icositetrahedron

• twelve-faced trapezohedron

• Trapezohedron on Wolfram MathWorld