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In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure. This implies that each vertex is surrounded by the same kinds of face in the same or reverse order, and with the same angles between corresponding faces.
In geometry, a polygon is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain. These segments are called its edges or sides, and the points where two of the edges meet are the polygon's vertices (singular: vertex) or corners.
In Euclidean geometry, an equiangular polygon is a polygon whose vertex angles are equal. If the lengths of the sides are also equal (that is, if it is also equilateral) then it is a regular polygon. Isogonal polygons are equiangular polygons which alternate two edge lengths. For clarity, a planar equiangular polygon can be called direct or ...
An isogon may refer to: Isogonal figure - a polygon or polyhedron with all of its vertices equivalent under the symmetries of the figure.
Computing the maximum number of equiangular lines in n-dimensional Euclidean space is a difficult problem, and unsolved in general, though bounds are known. The maximal number of equiangular lines in 2-dimensional Euclidean space is 3: we can take the lines through opposite vertices of a regular hexagon, each at an angle 120 degrees from the other two.
In Euclidean geometry, a regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex or star.
It was a compelling demonstration of how readily one can use physical and geometric principles in trying to understand biology. This was a major contribution in 1917 when vitalism was still being defended by prominent biologists. The battle was as won as it is ever likely to be by the time of the 1942 edition.
Onymacris unguicularis beetle with landmarks for morphometric analysis. In landmark-based geometric morphometrics, the spatial information missing from traditional morphometrics is contained in the data, because the data are coordinates of landmarks: discrete anatomical loci that are arguably homologous in all individuals in the analysis (i.e. they can be regarded as the "same" point in each ...