Search results
Results from the WOW.Com Content Network
Download as PDF; Printable version; In other projects ... Image Coxeter diagrams 1 4 6 12 24 Cells {p,3} It is also part of ... hexagon {6} Vertex figure: irregular ...
The following 14 pages use this file: Euclidean plane; Hexagonal tiling; List of regular polytopes; Rhombitrihexagonal tiling; Runcinated 5-cubes; Truncated trihexagonal tiling
A regular skew hexagon seen as edges (black) of a triangular antiprism, symmetry D 3d, [2 +,6], (2*3), order 12. A skew hexagon is a skew polygon with six vertices and edges but not existing on the same plane. The interior of such a hexagon is not generally defined. A skew zig-zag hexagon has vertices alternating between two parallel planes.
This includes the 3 regular tiles (triangle, square and hexagon) and 8 irregular ones. [4] Each vertex has edges evenly spaced around it. Three dimensional analogues of the planigons are called stereohedrons. These dual tilings are listed by their face configuration, the number of faces at each vertex of a face.
Note on Vertex figure images: The white polygon lines represent the "vertex figure" polygon. The colored faces are included on the vertex figure images help see their relations. Some of the intersecting faces are drawn visually incorrectly because they are not properly intersected visually to show which portions are in front.
Hexagonal tiling is the densest way to arrange circles in two dimensions. The honeycomb conjecture states that hexagonal tiling is the best way to divide a surface into regions of equal area with the least total perimeter.
The full symmetry of the regular form is r48 and no symmetry is labeled a1. The dihedral symmetries are divided depending on whether they pass through vertices ( d for diagonal) or edges ( p for perpendiculars), and i when reflection lines path through both edges and vertices.
The Weaire–Phelan structure contains another form of this polyhedron that has D 2d symmetry and is a part of a space-filling honeycomb along with an irregular dodecahedron. Irregular tetradecahedron