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Disdyakis dodecahedron
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== Related polyhedra and tilings == {| class=wikitable align=right width=320 |[[File:Conway polyhedron m3O.png|160px]] |[[File:Conway polyhedron m3C.png|160px]] |- |colspan=2|Polyhedra similar to the disdyakis dodecahedron are duals to the [[Symmetrohedron|Bowtie octahedron and cube]], containing extra pairs triangular faces .<ref>[http://www.cgl.uwaterloo.ca/csk/papers/bridges2001.html Symmetrohedra: Polyhedra from Symmetric Placement of Regular Polygons] Craig S. Kaplan</ref> |} The disdyakis dodecahedron is one of a family of duals to the uniform polyhedra related to the cube and regular octahedron. {{Octahedral truncations}} It is a polyhedra in a sequence defined by the [[face configuration]] V4.6.2''n''. This group is special for having all even number of edges per vertex and form bisecting planes through the polyhedra and infinite lines in the plane, and continuing into the hyperbolic plane for any ''n'' β₯ 7. With an even number of faces at every vertex, these polyhedra and tilings can be shown by alternating two colors so all adjacent faces have different colors. Each face on these domains also corresponds to the fundamental domain of a [[symmetry group]] with order 2,3,''n'' mirrors at each triangle face vertex. {{Omnitruncated table}} {{Omnitruncated4 table}}
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