Is every regular polygon the unit ball for some norm?

Question

For every regular polygon, is there a norm such that the polygon is it's unit ball centered on 0?

Since $|-x|=|x|$, this cetainly fails for odd-gons. – Hagen von Eitzen Nov 23 '14 at 18:42 — Hagen von Eitzen, Nov 23 '14 at 18:42

score 4 · Answer 1 · edited Apr 13 '17 at 12:20

4

Since $\|-x\|=\|x\|$, this cetainly fails for odd-gons. -- Hagen von Eitzen

On the other hand, it holds for even number of sides. See Minkowski functional.

edited Apr 13 '17 at 12:20

Community

answered Dec 27 '14 at 21:23

Can you please explain how the minkowski functional related to it? we covered it briefly in our functional analysis course but I don't see the connection. – ViktorStein Jun 01 '19 at 22:13

1 Answers1