unequal n-antiprism, with the top and bottom n-gons of different radii. If the kites are twisted and are of two different shapes, the n-trapezohedron can only have Cn (cyclic) symmetry, order n, and is called an unequal twisted trapezohedron. Star trapezohedron A star -trapezohedron (where ) is defined by a regular zig-zag skew star -gon base, two symmetric apices with no degree of freedom right above and right below the base, and quadrilateral faces connecting each pair of adjacent basal edges to one apex. A star -trapezohedron has two apical vertices on its polar axis, and basal vertices in two regular -gonal rings. It has congruent kite faces, and it is isohedral. Such a star -trapezohedron is a self-intersecting, crossed, or non-convex form. It exists for any regular zig-zag skew star -gon base (where ). But if , then , so the dual star antiprism (of the star trapezohedron) cannot be uniform (i.e. cannot have equal edge lengths); and if , then , so the dual star antiprism must be flat, thus degenerate, to be uniform. A dual-uniform star -trapezohedron has Coxeter-Dynkin diagram . See also Diminished trapezohedron Rhombic dodecahedron Rhombic triacontahedron Bipyramid Truncated trapezohedron Conway polyhedron notation The Haunter of the Dark, a short story by H.P. Lovecraft in which a fictional ancient artifact known as The Shining Trapezohedron plays a crucial role. References Chapter 4: Duals of the Archimedean polyhedra, prisma and antiprisms External links Virtual Reality Polyhedra The Encyclopedia of Polyhedra VRML models (George Hart) <3> <4> <5> <6> <7> <8> <9> <10> Conway Notation for Polyhedra Try: "dAn", where n=3,4,5... Example: "dA5" is a pentagonal trapezohedron. Paper model tetragonal (square) trapezohedron Polyhedra fr:Antidiamant