Properties Rhombic dodecahedron



a garnet crystal


the rhombic dodecahedron can used tessellate three-dimensional space. can stacked fill space hexagons fill plane.


this polyhedron in space-filling tessellation can seen voronoi tessellation of face-centered cubic lattice. brillouin zone of body centered cubic (bcc) crystals. minerals such garnet form rhombic dodecahedral crystal habit. honey bees use geometry of rhombic dodecahedra form honeycombs tessellation of cells each of hexagonal prism capped half rhombic dodecahedron. rhombic dodecahedron appears in unit cells of diamond , diamondoids. in these cases, 4 vertices (alternate threefold ones) absent, chemical bonds lie on remaining edges.


the graph of rhombic dodecahedron nonhamiltonian.


a rhombic dodecahedron can dissected center 4 trigonal trapezohedra. these rhombohedra cells of trigonal trapezohedral honeycomb. analogous dissection of regular hexagon dissected rhombi, , tiled in plane rhombille.









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