Search results
Results from the WOW.Com Content Network
The rhombic dodecahedron can be seen as a degenerate limiting case of a pyritohedron, with permutation of coordinates (±1, ±1, ±1) and (0, 1 + h, 1 − h 2) with parameter h = 1. These coordinates illustrate that a rhombic dodecahedron can be seen as a cube with six square pyramids attached to each face, allowing them to fit together into a ...
The vertices with the obtuse rhombic face angles have 4 cells. The vertices with the acute rhombic face angles have 6 cells. The rhombic dodecahedron can be twisted on one of its hexagonal cross-sections to form a trapezo-rhombic dodecahedron, which is the cell of a somewhat similar tessellation, the Voronoi diagram of hexagonal close-packing.
1 space filling oblate octa Cuboctahedron 2.5 edges 1/2, vol. = 1/8 of 20 Duo-Tet Cube 3 24 MITEs Octahedron 4 dual of cube, spacefills w/ tet Rhombic Triacontahedron 5 radius = ~0.9994, vol. = 120 Ts Rhombic Triacontahedron 5+ radius = 1, vol. = 120 Es Rhombic Dodecahedron 6 space-filler, dual to cuboctahedron Rhombic Triacontahedron 7.5 ...
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 ...
There are five types of parallelohedron, first identified by Evgraf Fedorov in 1885 in his studies of crystallographic systems: the cube, hexagonal prism, rhombic dodecahedron, elongated dodecahedron, and truncated octahedron. Each parallelohedron is a zonohedron and a plesiohedron. It has point reflection symmetry, as do its faces.
Its Voronoi cell is a rhombic dodecahedron, the dual of the cuboctahedron vertex figure for the tet-oct honeycomb. The D + 3 packing can be constructed by the union of two D 3 (or A 3) lattices. The D + n packing is only a lattice for even dimensions. The kissing number is 2 2 =4, (2 n-1 for n<8, 240 for n=8, and 2n(n-1) for n>8). [4] ∪ . The ...
The uploader of this file has agreed to the Wikimedia Foundation 3D patent license: This file and any 3D objects depicted in the file are both my own work. I hereby grant to each user, maker, or distributor of the object depicted in the file a worldwide, royalty-free, fully-paid-up, nonexclusive, irrevocable and perpetual license at no additional cost under any patent or patent application I ...
where φ = 1 + √ 5 / 2 is the golden ratio. Therefore, the circumradius of this rhombicosidodecahedron is the common distance of these points from the origin, namely √ φ 6 +2 = √ 8φ+7 for edge length 2. For unit edge length, R must be halved, giving R = √ 8φ+7 / 2 = √ 11+4 √ 5 / 2 ≈ 2.233.