The rhombic dodecahedral honeycomb (also dodecahedrille) is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It is the Voronoi diagram of the face-centered cubic sphere-packing, which has the densest possible packing of equal spheres in ordinary space (see Kepler conjecture).
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The rhombicdodecahedralhoneycomb (also dodecahedrille) is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It is the Voronoi diagram...
stellated rhombicdodecahedralhoneycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of copies of stellated rhombic dodecahedron...
related to the rhombicdodecahedralhoneycomb with an elongation of zero. Projected normal to the elongation direction, the honeycomb looks like a square...
can tessellate space to form the stellated rhombicdodecahedralhoneycomb. The first stellation of the rhombic dodecahedron has 12 faces, each of which...
or the rhombic triacontahedron or the rhombicdodecahedralhoneycomb or the rhombic icosahedron or the rhombic hexecontahedron or the rhombic enneacontahedron...
centered cubic (bcc) crystals. Some minerals such as garnet form a rhombicdodecahedral crystal habit. As Johannes Kepler noted in his 1611 book on snowflakes...
achieved by putting a rhombicuboctahedron in each cell of the rhombicdodecahedralhoneycomb, and it cannot be surpassed, since otherwise the optimal packing...
the four long diagonals of a cube. It tiles space to form the rhombicdodecahedralhoneycomb. The elongated dodecahedron, generated from five line segments...
achieved by putting a rhombicuboctahedron in each cell of the rhombicdodecahedralhoneycomb, and it cannot be surpassed, since otherwise the optimal packing...
has a rhombicdodecahedral envelope. Two vertices of the tesseract are projected to the origin. There are exactly two ways of dissecting a rhombic dodecahedron...
as a partial hexagonal honeycomb, but all vertices will not match. The rhombic dodecahedron is a zonohedron with twelve rhombic faces and octahedral symmetry...
honeycomb and the plesiohedron generated by the diamond lattice The trapezo-rhombic dodecahedron, the prototile of the trapezo-rhombicdodecahedral honeycomb...
is said to be noble. Not all isozonohedra are isohedral. For example, a rhombic icosahedron is an isozonohedron but not an isohedron. A polyhedron (or...
can be considered a transitional phase between the cubic and rhombicdodecahedralhoneycombs. Here, the cells are colored white, red, and blue based on...
2D Euclidean space. Its three dimensional equivalent is the rhombicdodecahedralhoneycomb, derived from the most dense packing of spheres in 3D Euclidean...
cases include the Euclidean cubic honeycomb {4,3,4} with cubic cells, and compact hyperbolic {5,3,4} with dodecahedral cells, and paracompact {6,3,4} with...
the rhombicdodecahedralhoneycomb. Six diminished points come together to form cubic holes. It has 13 of 14 Cartesian coordinates of the rhombic dodecahedron...
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