Non-Wythoffian Constructions
Uniform polytopes that can't be created through a Wythoff mirror construction are called non-Wythoffian. They generally can be derived from Wythoffian forms either by alternation (deletion of alternate vertices) or by insertion of alernating layers of partial figures. Both of these types of figures will contain rotational symmetry. Sometimes snub forms are considered Wythoffian, even though they can only be constructed by the alternation of omnitruncated forms.
The hexagonal antiprism is constructed by an alternation of a dodecagonal prism. |
The elongated triangular tiling is constructed by a layering of square tiling and triangular tiling rows. |
The great dirhombicosidodecahedron is the only non-Wythoffian uniform polyhedron. |
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