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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 ...
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 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.
6 - regular hexagon; 8 - regular octagon; 10 - regular decagon; 5/2 - pentagram; 8/3 - octagram; 10/3 - decagram; Some faces will appear with reverse orientation which is written here as -3 - a triangle with reverse orientation (often written as 3/2) Others pass through the origin which we write as 6* - hexagon passing through the origin
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