![]() In the plane, Therefore, there are only three regular tessellations (composed of the hexagon, square, and triangle ), illustrated above (Ghyka 1977, p. You have a single vertex, which has edges to the triangle surrounding it.Īs for the edges between triangles, that's just how it converts the various tessellated points to create a full set of triangles. Consider a two-dimensional tessellation with regular -gons at each polygon vertex. Which is exactly what you have in the center. Now we have a Zen Koan: what does a triangle with no edges look like? And the second will be tessellated into 4 - 2 * 2 = 0 edges. The first inner triangle will be tessellated into 4 - 2 * 1 = 2 edges. If you have, as in your case, N=4, then there will be 2 inner triangles. The first inner triangle will have 3 edges and the second will have 1.īut something odd happens in this equations when N is even. So if we have an inner tessellation level of 5, then there will be 2 inner triangles. The number of edges that an inner triangle edge is tessellated into is N - 2K. The edges of an inner triangle are always tessellated into the same number of edges. K therefore represents each concentric inner triangle, with K = 1 representing the outermost inner triangle (but not the outer triangle). ![]() And let K go from 1 to N/2, rounded down. But the number of concentric triangles generated is half of the inner tessellation level, rounded down. By definition, a tessellation is tiling that uses shapes to cover a surface with no gaps or overlaps. Triangle tessellation is defined based on generating concentric triangles within the outer triangle. I suppose the confusing part is how the inner tessellation level works. By definition, tilings require the use of regular polygons put together such that it completely. A second is tessellated into 2 edges and the third into three. There is a difference between a tiling and a tessellation. Therefore, one edge is "subdivided" into one edge. Voronoi or Dirichlet tilings are tessellations where each tile is defined as the set of points closest to one of the points in a discrete set of defining points. You provided the tessellation levels 1, 2, and 3. Each edge is assigned an index in the outer tessellation levels array, as specified in the standard. ![]() Therefore, a tessellation level of 1 means one edge. The tessellation levels specify the number of edges that will be generated. ![]()
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