Rhombic dodecahedron
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In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of 2 types. As a Catalan solid, it is the dual polyhedron of the cuboctah
A garnet crystal
Modell, Kristallform Deltoiddodekaeders Krantz
Honeycomb (geometry)
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In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of the more general mathematical tiling or tessellat
Rhombic dodecahedron
…vertices of 2 types. As a Catalan solid, it is the dual polyhedron of the cuboctahedron. As a parallelohedron, the rhombic dodecahedron can be used to tesselate its copies in space creating a rhombic dodecahedral honeycomb. There are some variations of the rhombic dodecahedron, one of which is the Bilinski dodecahedron. There are…
It is possible to fill the plane with polygons which do not meet at their corners, for example using rectangles, as in a brick wall pattern: this is not a proper tiling because corners lie part way along the edge of a neighbouring polygon. Similarly, in a proper honeycomb, there must be no edges or vertices lying part way along the face of a neighbouring cell. Interpreting each brick face as a hexagon having two interior angles of 180 degrees allows the pattern to be considered as a proper tiling. However, not all geometers accept such hexagons.