Who is the king of the polygons?

[Pondlife]

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[doodab]

All of those options are regular polygons. Sounds like prejudice towards the irregular to me.

I prefer a good concave polygon myself.

You can have an irregular concave pentagon or above. A square, I will grant you, is regular.

[TheFaQQer]

I refuse to accept a henagon as a polygon.

Hendecagon, yes. However, my personal favourite (and therefore the logical ruler of all) is the chiliagon.

[TheFaQQer]

All of those options are regular polygons. Sounds like prejudice towards the irregular to me.

No they aren't - there is nothing in the list which dictates line length and angle size.

If you accept a henagon as a polygon, then obviously that is the exception, since they are all regular by definition.

[VectraMan]

No they aren't - there is nothing in the list which dictates line length and angle size.

I think in the minds of most people, "pentagon" for example refers to a regular pentagon. The famous US government building isn't known as "The Regular Pentagon".

If you're going to take "pentagon" to mean any 5 sided polygon, then there are limitless possibilities, and that makes the question entirely stupid.

[doodab]

I think in the minds of most people, "pentagon" for example refers to a regular pentagon. The famous US government building isn't known as "The Regular Pentagon".

If you're going to take "pentagon" to mean any 5 sided polygon, then there are limitless possibilities, and that makes the question entirely stupid.

Well, that is what pentagon means. It's quite acceptable to call a regular pentagon a pentagon, because it is.

[NickFitz]

The famous US government building isn't known as "The Regular Pentagon".

That's because the American People wouldn't accept a regular pentagon. They'd demand an extra-large pentagon, with a side order of fries.

[TheFaQQer]

That's because the American People wouldn't accept a regular pentagon. They'd demand an extra-large pentagon, with a side order of fries.

You must spread some Reputation around before giving it to NickFitz again.

[Ignis Fatuus]

I think in the minds of most people, "pentagon" for example refers to a regular pentagon. The famous US government building isn't known as "The Regular Pentagon".

If you're going to take "pentagon" to mean any 5 sided polygon, then there are limitless possibilities, and that makes the question entirely stupid.

With respect, what most people call something is not the guiding principle in mathematics.

And from (for example) a topology point of view, all pentagons that do not intersect themselves are one and the same.

(Pentagons where each side intersects 2 other sides are different from that, but the same as each other. Do you know any other kinds of pentagon apart from those two?)

Isomorphism is the essence of mathematics, and of symmetry, and of understanding the universe.