Question: How to define complex region of 3D plotting of function f(x,y)?


I need to plot some function f(x,y) on a right hexagon pllaced on (x,y)-plane. I can define my hexagon in following way:

if -(4*pi)/3/sqrt(3)<x<(2*pi)/3/sqrt(3) then -sqrt(3)*(x-4*pi/3/sqrt(3))<y<sqrt(3)*(x-4*pi/3/sqrt(3))

if -(2*pi)/3/sqrt(3)<x<(2*pi)/3/sqrt(3) then -2*pi/3<y<2*pi/3

if (2*pi)/3/sqrt(3)<x<(4*pi)/3/sqrt(3) then -sqrt(3)*(4*pi/3/sqrt(3)-x)<y<sqrt(3)*(4*pi/3/sqrt(3)-x)

My haxagon looks like

I want to 3D plot a function defined on this hexagon

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