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An equiangular hexagon with 1:2 edge length ratios, with equilateral triangles. [6] This is spirolateral 2 120°. Direct equiangular hexagons, <6> and <6/2>, have 120° and 60° internal angles respectively. 120° internal angles of an equiangular hexagon, <6> An equiangular hexagon with integer side lengths may be tiled by unit equilateral ...
A non-convex regular polygon is a regular star polygon. The most common example is the pentagram, which has the same vertices as a pentagon, but connects alternating vertices. For an n-sided star polygon, the Schläfli symbol is modified to indicate the density or "starriness" m of the polygon, as {n/m}.
The polygon is the convex hull of its edges. Additional properties of convex polygons include: The intersection of two convex polygons is a convex polygon. A convex polygon may be triangulated in linear time through a fan triangulation, consisting in adding diagonals from one vertex to all other vertices.
There are 7 subgroup dihedral symmetries: (Dih 12, Dih 6, Dih 3), and (Dih 8, Dih 4, Dih 2 Dih 1), and 8 cyclic group symmetries: (Z 24, Z 12, Z 6, Z 3), and (Z 8, Z 4, Z 2, Z 1). These 16 symmetries can be seen in 22 distinct symmetries on the icositetragon. John Conway labels these by a letter and group order. [2]
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. A regular skew hexagon is vertex-transitive with equal edge lengths.
With a final vertex 3 4.6, 4 more contiguous equilateral triangles and a single regular hexagon. However, this notation has two main problems related to ambiguous conformation and uniqueness [ 2 ] First, when it comes to k-uniform tilings, the notation does not explain the relationships between the vertices.
However, Eberhard's theorem states that it should be possible to form a simple polyhedron by adding some number of hexagons, and in this case one hexagon suffices: bisecting a cube on a regular hexagon passing through six of its faces produces two copies of a simple roofless polyhedron with three triangle faces, three pentagon faces, and one ...
The convex hull of a simple polygon (blue). Its four pockets are shown in yellow; the whole region shaded in either color is the convex hull. In discrete geometry and computational geometry, the convex hull of a simple polygon is the polygon of minimum perimeter that contains a given simple polygon.