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An example of a concave polygon. A simple polygon that is not convex is called concave, [1] non-convex [2] or reentrant. [3] A concave polygon will always have at least one reflex interior angle—that is, an angle with a measure that is between 180 degrees and 360 degrees exclusive. [4]
The elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body.
It is an example of a hedgehog, a type of curve determined as the envelope of a system of lines with a continuous support function. The hedgehogs also include non-convex curves, such as the astroid, and even self-crossing curves, but the smooth strictly convex curves are the only hedgehogs that have no singular points. [33]
The shrinking process, the straight skeleton (blue) and the roof model. In geometry, a straight skeleton is a method of representing a polygon by a topological skeleton.It is similar in some ways to the medial axis but differs in that the skeleton is composed of straight line segments, while the medial axis of a polygon may involve parabolic curves.
The simplest polygon which can cross itself; the simplest polygon which can be concave; the simplest polygon which can be non-cyclic. Can tile the plane. pentagon: 5 [21] The simplest polygon which can exist as a regular star. A star pentagon is known as a pentagram or pentacle. hexagon: 6 [21] Can tile the plane. heptagon (or septagon) 7
In the mathematical theory of hypergraphs, a hedgehog is a 3-uniform hypergraph defined from an integer parameter . It has t + ( t 2 ) {\displaystyle t+{\tbinom {t}{2}}} vertices, t {\displaystyle t} of which can be labeled by the integers from 1 {\displaystyle 1} to t {\displaystyle t} and the remaining ( t 2 ) {\displaystyle {\tbinom {t}{2 ...
A hedgehog is a spiny mammal of the ... they have adapted to a nocturnal way of life. [3] ... it was reported that the hedgehog population in rural Britain was ...
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.