what's cyclically ordered set? Are solid bodies have cyclically ordered set of point?

shahar

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A polygon is a geometric object consisting of anumber of points, vertices, and an equal number of line segments, sides, namelya cyclically ordered set of points in a plane, with no three successive pointscollinear, together with the line segments joining consecutive pairs of the points.
What is cyclically ordered set of point?
Are solid bodies have cyclically ordered set of point?
 
A polygon is a geometric object consisting of a number of points, vertices, and an equal number of line segments, sides, namely a cyclically ordered set of points in a plane, with no three successive points collinear, together with the line segments joining consecutive pairs of the points.
What is cyclically ordered set of point?
Are solid bodies have cyclically ordered set of point?

Did you try searching for the phrase "cyclically ordered set"? I was taken to Wikipedia. You don't need to look beyond the first two paragraphs to see what it means.

Basically, it means that you can list them in order and come back to the start.

A solid body, such as a polyhedron, will not have vertices in such an order as part of their definition. Of course, you can put any set of points in cyclic order, but that would not include all the edges.
 
Did you try searching for the phrase "cyclically ordered set"? I was taken to Wikipedia. You don't need to look beyond the first two paragraphs to see what it means.

Basically, it means that you can list them in order and come back to the start.

A solid body, such as a polyhedron, will not have vertices in such an order as part of their definition. Of course, you can put any set of points in cyclic order, but that would not include all the edges.
There is a proof that polygon have cyclic order? [Even in Advanced Math?]
 
There is a proof that polygon have cyclic order? [Even in Advanced Math?]

There is no need for a proof; it is a definition! What you quoted was such a definition, right? If the edges don't proceed from one vertex to another cyclically, then we just don't call it a polygon.
 
A polygon is a geometric object consisting of anumber of points, vertices, and an equal number of line segments, sides, namelya cyclically ordered set of points in a plane, with no three successive pointscollinear, together with the line segments joining consecutive pairs of the points.
What is cyclically ordered set of point?
Are solid bodies have cyclically ordered set of point?
Polygons are 2-D structure. Solid bodies are 3-D structure.
 
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