mjhjmtu

To illustrate what edge-coloring is, I'd like to colorize a regular polygon. I want to generate the shape using TikZ, then colorize the sides (edges) of the polygon separately, for instance by doing something like this:

draw[red] (polygon.side 1);

Unfortunately, the world does not seem to work like this. For now my ugly workaround is to overdraw using dotted, dashed, and thick lines.

documentclassstandalone
usepackagetikz
usetikzlibraryshapes.geometric,positioning

begindocument
begintikzpicture
 node[draw, dotted, minimum size=2cm, regular polygon,
 regular polygon sides=5] (polygon) ;
 draw[thick] (polygon.corner 1) -- (polygon.corner 2);
 draw[dashed] (polygon.corner 2) -- (polygon.corner 3);
 draw[thick] (polygon.corner 4) -- (polygon.corner 5);
 draw[dashed] (polygon.corner 5) -- (polygon.corner 1);
endtikzpicture
enddocument

Thanks!

With regular polygon colors option, there's no need for extra commands to draw the sides. Everything is done within the node command.

documentclass[tikz,border=3.14mm]standalone
usetikzlibraryshapes.geometric, positioning

begindocument
begintikzpicture[
regular polygon colors/.style 2 args=
 append after command=%
 pgfextra
 foreach i [count=ni, remember=ni as lasti (initially #1)] in #2
 draw[i] (tikzlastnode.corner lasti) --(tikzlastnode.corner ni);
 endpgfextra
 
,
]
 node[minimum size=2cm, regular polygon,
 regular polygon sides=5, 
 regular polygon colors=5red,blue,orange,green,cyan] (polygon) ;

 node[minimum size=2cm, regular polygon,
 regular polygon sides=7, 
 regular polygon colors=7red, blue, orange, green, cyan, violet, brown,
 right=of polygon] (polygon2) ;
endtikzpicture

enddocument

Like this?

documentclass[margin=1mm]standalone
usepackagetikz

begindocument
begintikzpicture[thick]
foreach i/c in 90/red,162/blue,234/green,306/pink,378/orange
 draw[c] (i:1cm) -- (72+i:1cm);

endtikzpicture
enddocument

Edit 1: Another option, to have a better join line:

begintikzpicture[thick]
foreach i/c in 90/red,162/blue,234/green,306/pink,378/orange
fill[c] (i:1cm) -- (72+i:1cm) -- (0,0) -- cycle;

fill[white] (90:.95cm)--(162:.95cm)--(234:.95cm)--(306:.95cm)--(378:.95cm)--cycle;
endtikzpicture

Edit 2: just for fun.

begintikzpicture
foreach r in 1,.9,...,.1
pgfmathparse30 * r%
pgfmathsetmacropercentpgfmathresult
foreach i/c in 90/red,162/blue,234/green,306/pink,378/orange
fill[c!percent] (i:r cm) -- (72+i:r cm) -- (0,0) -- cycle;

endtikzpicture

Here is a proposal that defines a style polygon side which can be used e.g. like draw[red,polygon side=2]; to draw the second side red.

documentclass[tikz,border=3.14mm]standalone
usetikzlibraryshapes.geometric

begindocument
begintikzpicture[get next vertex/.code n args=2%
pgfmathparseint(1+mod(#1,5))
xdef#2pgfmathresult,
polygon side/.style=get next vertex=#1tmpnextn,
insert path=(polygon.corner #1)-- (polygon.corner tmpnextn)
]
 node[draw, dotted, minimum size=2cm, regular polygon,
 regular polygon sides=5] (polygon) ;
 foreach X [count=Y] in red,blue,orange,green,cyan
 draw[X,polygon side=Y];
endtikzpicture
enddocument

Note that as of now the number of corners (or sides) as well as the name of the object (or node), polygon, are hard coded. One could of course use pgfkeys to store them in some keys, and if you ask me to I'll be happy to add this to this answer.