imagepolygon

Function to get 5-sided polygon (pentagon) or star (pentagram) co-ords. 
<?php
function _makeFiveSidedStar( $x, $y, $radius, $shape='polygon', $spiky=NULL ) {
    $point = array() ; // new array                                                                                                                   
    $angle = 360 / 5 ;                                                                                                                    
    $point[0]['x'] = $x ;                                                                                                                 
    $point[0]['y'] = $y - $radius ;                                                                                                       
    $point[2]['x'] = $x + ( $radius * cos( deg2rad( 90 - $angle ) ) ) ; 
    $point[2]['y'] = $y - ( $radius * sin( deg2rad( 90 - $angle ) ) ) ;
    $point[4]['x'] = $x + ( $radius * sin( deg2rad( 180 - ( $angle*2 ) ) ) ) ;
    $point[4]['y'] = $y + ( $radius * cos( deg2rad( 180 - ( $angle*2 ) ) ) ) ;
    $point[6]['x'] = $x - ( $radius * sin( deg2rad( 180 - ( $angle*2 ) ) ) ) ;                                                            
    $point[6]['y'] = $y + ( $radius * cos( deg2rad( 180 - ( $angle*2 ) ) ) ) ;
    $point[8]['x'] = $x - ( $radius * cos( deg2rad( 90 - $angle ) ) ) ;                                                                   
    $point[8]['y'] = $y - ( $radius * sin( deg2rad( 90 - $angle ) ) ) ;
    if( $shape == 'star' ) {
        if( $spiky == NULL ) $spiky = 0.5 ;  // degree of spikiness, default to 0.5
        $indent = $radius * $spiky ;
        $point[1]['x'] = $x + ( $indent * cos( deg2rad( 90 - $angle/2 ) ) ) ;                                                             
        $point[1]['y'] = $y - ( $indent * sin( deg2rad( 90 - $angle/2 ) ) ) ;                                                     
        $point[3]['x'] = $x + ( $indent * sin( deg2rad( 180 - $angle ) ) ) ;                                                              
        $point[3]['y'] = $y - ( $indent * cos( deg2rad( 180 - $angle ) ) ) ;
        $point[5]['x'] = $x ;                                                                                                             
        $point[5]['y'] = $y + ( $indent * sin( deg2rad( 180 - $angle ) ) ) ;
        $point[7]['x'] = $x - ( $indent * sin( deg2rad( 180 - $angle ) ) ) ;                                                              
        $point[7]['y'] = $y - ( $indent * cos( deg2rad( 180 - $angle ) ) ) ;                                                              
        $point[9]['x'] = $x - ( $indent * cos( deg2rad( 90 - $angle/2 ) ) ) ;                                                             
        $point[9]['y'] = $y - ( $indent * sin( deg2rad( 90 - $angle/2 ) ) ) ;
    }
    ksort( $point ) ;
    $coords = array() ;  // new array                                                                                                                 
    foreach( $point as $pKey=>$pVal ) {                                                                                                   
        if( is_array( $pVal ) ) {                                                                                                         
            foreach( $pVal as $pSubKey=>$pSubVal ) {                                                                                      
                if( !empty( $pSubVal ) ) array_push( $coords, $pSubVal ) ;                                                                
            }                                                                                                                             
        }                                                                                                                                 
    }
    return $coords ;
}
$values = _makeFiveSidedStar( 100, 100, 50, 'star' ) ;
?>

Function to draw a n-sided regular polygon

<?php
$img = imagecreatetruecolor(1360,768);

function regularPolygon($img,$x,$y,$radius,$sides,$color)
{
    $points = array();
    for($a = 0;$a <= 360; $a += 360/$sides)
    {
        $points[] = $x + $radius * cos(deg2rad($a));
        $points[] = $y + $radius * sin(deg2rad($a));
    }
    return imagepolygon($img,$points,$sides,$color);
}

regularPolygon($img,1360/2,768/2,300,8,0xffffff);//Test draw

header('Content-type: image/png');
imagepng($img);
imagedestroy($img);
?>

Here are some handy routines for rotation and translation of polygons.  Scaling could be added easily as well.

<?php
function translate_point(&$x,&$y,$angle,$about_x,$about_y,$shift_x,$shift_y)
{
    $x -= $about_x;
    $y -= $about_y;
    $angle = ($angle / 180) * M_PI;
/* math:
[x2,y2] = [x,  *  [[cos(a),-sin(a)],
           y]      [sin(a),cos(a)]]
==>
x = x * cos(a) + y*sin(a) 
y = x*-sin(a) + y*cos(a)
*/

    $new_x = $x * cos($angle) - $y * sin($angle);
    $new_y = $x * sin($angle) + $y * cos($angle);
    $x = $new_x+ $about_x + $shift_x ;
    $y = $new_y + $about_y + $shift_y;
}

function translate_poly($point_array, $angle, $about_x, $about_y,$shift_x,$shift_y)
{
    $translated_poly = Array();
    while(count($point_array) > 1)
    {
        $temp_x = array_shift($point_array);
        $temp_y = array_shift($point_array);
        translate_point($temp_x, $temp_y, $angle, $about_x, $about_y,$shift_x, $shift_y);
        array_push($translated_poly, $temp_x);
        array_push($translated_poly, $temp_y);
    }
    return $translated_poly;
}
?>