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The term complex polygon can mean two different things:
- In computer graphics, as a polygon which is neither convex nor concave.
- In geometry, as a polygon in the unitary plane, which has two complex dimensions.
- Has a boundary comprising discrete circuits, such as a polygon with a hole in it.
Therefore, unlike simple polygons, a complex polygon may not always be interpreted as a simple polygonal region. Vertices are only counted at the ends of edges, not where edges intersect in space.
A formula relating an integral over a bounded region to a closed line integral may still apply when the "inside-out" parts of the region are counted negatively.
Moving around the polygon, the total amount one "turns" at the vertices can be any integer times 360°, e.g. 720° for a pentagram and 0° for an angular "eight".
A complex number may be represented in the form , where and are real numbers, and is the square root of . A complex number lies in a complex plane having one real and one imaginary dimension, which may be represented as an Argand diagram. So a single complex dimension is really two dimensions, but of different kinds.
A complex polygon is a two-dimensional example of the more general complex polytope in higher dimensions.
In a real plane, a visible figure can be constructed as the real conjugate of some complex polygon.
- Coxeter, H. S. M., Regular Complex Polytopes, Cambridge University Press, 1974.
- Simple polygon
- Convex and concave polygons
- Star polygon
- Convex hull
- Nonconvex uniform polyhedron
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