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A truncated hexagon, t{6}, is a dodecagon, {12}, alternating two types (colors) of edges. An alternated hexagon, h{6}, is an equilateral triangle, {3}. A regular hexagon can be stellated with equilateral triangles on its edges, creating a hexagram. A regular hexagon can be dissected into six equilateral triangles by adding a
Breaking a polygon into monotone polygons. A simple polygon is monotone with respect to a line L, if any line orthogonal to L intersects the polygon at most twice. A monotone polygon can be split into two monotone chains. A polygon that is monotone with respect to the y-axis is called y-monotone.
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 optimal three-dimensional structure for making honeycomb (or rather, soap bubbles) was investigated by Lord Kelvin , who believed that the Kelvin structure (or body-centered cubic lattice) is ...
It is possible to divide an equilateral triangle into three congruent non-convex pentagons, meeting at the center of the triangle, and to tile the plane with the resulting three-pentagon unit. [21] A similar method can be used to subdivide squares into four congruent non-convex pentagons, or regular hexagons into six congruent non-convex ...
It can be seen as an equilateral hexagonal tiling with each hexagon divided into 12 triangles from the center point. (Alternately it can be seen as a bisected triangular tiling divided into 6 triangles, or as an infinite arrangement of lines in six parallel families.)
3 constructions for a {3,5+} 6,0; An icosahedron and related symmetry polyhedra can be used to define a high geodesic polyhedron by dividing triangular faces into smaller triangles, and projecting all the new vertices onto a sphere. Higher order polygonal faces can be divided into triangles by adding new vertices centered on each face.
Also, as an equilateral triangle is a hexagon and three smaller equilateral triangles it is possible to superimpose a large polyiamond on any polyhex, giving two polyiamonds corresponding to each polyhex. This is used as the basis of an infinite division of a hexagon into smaller and smaller hexagons (an irrep-tiling) or into hexagons and ...
A hexagon also has 6 edges as well as 6 internal and external angles. 6 is the second smallest composite number. [1] It is also the first number that is the sum of its proper divisors, making it the smallest perfect number. [2] 6 is the first unitary perfect number, since it is the sum of its positive proper unitary divisors, without including ...