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As Johannes Kepler noted in his 1611 book on snowflakes (Strena seu de Nive Sexangula), honey bees use the geometry of rhombic dodecahedra to form honeycombs from a tessellation of cells each of which is a hexagonal prism capped with half a rhombic dodecahedron. The rhombic dodecahedron also appears in the unit cells of diamond and diamondoids ...
The 16-cell is the second in the sequence of 6 convex regular 4-polytopes (in order of size and complexity). [a]Each of its 4 successor convex regular 4-polytopes can be constructed as the convex hull of a polytope compound of multiple 16-cells: the 16-vertex tesseract as a compound of two 16-cells, the 24-vertex 24-cell as a compound of three 16-cells, the 120-vertex 600-cell as a compound of ...
In a point region (PR) octree, the node stores an explicit three-dimensional point, which is the "center" of the subdivision for that node; the point defines one of the corners for each of the eight children. In a matrix-based (MX) octree, the subdivision point is implicitly the center of the space the node represents.
The primitive rectangular lattice can also be described by a centered rhombic unit cell, while the centered rectangular lattice can also be described by a primitive rhombic unit cell. Note that the length a {\displaystyle a} in the lower row is not the same as in the upper row.
The cantitruncated 120-cell is a uniform polychoron. This 4-polytope is related to the regular 120-cell. The cantitruncation operation create new truncated tetrahedral cells at the vertices, and triangular prisms at the edges. The original dodecahedron cells are cantitruncated into great rhombicosidodecahedron cells.
Finally, a Sobel filter or similar edge-detection filter is applied to the normal and depth textures to generate an edge texture. Texels on detected edges are black, while all other texels are white. Finally, the edge texture and the color texture are composited to produce the final rendered image.
A mesh need not be simplicial because an arbitrary subset of nodes of a cell is not necessarily a cell: e.g., three nodes of a quad does not define a cell. However, two cells intersect at cells: e.g. a quad does not have a node in its interior. The intersection of two cells may be several cells: e.g., two quads may share two edges.
Winged-edge meshes address the issue of traversing from edge to edge, and providing an ordered set of faces around an edge. For any given edge, the number of outgoing edges may be arbitrary. To simplify this, winged-edge meshes provide only four, the nearest clockwise and counter-clockwise edges at each end.