I'll show you what i've been doing. I managed to make my program work, but i'm not gonna continue with the same way. So here's the code, i hope you're not going to laugh. Let's call this a robust attempt:

use GD;
use constant PI    => 4 * atan2(1, 1);
$ima = new GD::Image(800,800);
$black = $ima->colorAllocate(0,0,0);
$green=$ima->colorAllocate(0,255,0);
$ima->setThickness(3);
$data = $ima->gifanimbegin(1,0);

$im = new GD::Image(800,800);
$black = $im->colorAllocate(0,0,0);
$green=$im->colorAllocate(0,255,0);
$white=$im->colorAllocate(0,0,0);
$im->setThickness(3);
@een=(360,360,80);
@twee=(440,360,80);
@drie=(440,360,0);
@vier=(360,360,0);
$x1 =$een[0] + sqrt($een[2]**2/2);
$y1=$een[1] - sqrt($een[2]**2/2);
$x2 =$twee[0] + sqrt($twee[2]**2/2);
$y2=$twee[1] - sqrt($twee[2]**2/2);
$x3 =$drie[0] + sqrt($drie[2]**2/2);
$y3=$drie[1] - sqrt($drie[2]**2/2);
$x4 =$vier[0] + sqrt($vier[2]**2/2);
$y4=$vier[1] - sqrt($vier[2]**2/2);
$xx1=$x1;
$xx2=$x2;
$xx3=$x3;
$xx4=$x4;
$yy1=$y1+80;
$yy2=$y2+80;
$yy3=$y3+80;
$yy4=$y4+80;
$im->line($x1,$y1,$x2,$y2,$green);
$im->line($x2,$y2,$x3,$y3,$green);
$im->line($x3,$y3,$x4,$y4,$green);
$im->line($x4,$y4,$x1,$y1,$green);
$im->line($xx1,$yy1,$xx2,$yy2,$green);
$im->line($xx2,$yy2,$xx3,$yy3,$green);
$im->line($xx3,$yy3,$xx4,$yy4,$green);
$im->line($xx4,$yy4,$xx1,$yy1,$green);
$im->line($x1,$y1,$xx1,$yy1,$green);
$im->line($x2,$y2,$xx2,$yy2,$green);
$im->line($x3,$y3,$xx3,$yy3,$green);
$im->line($x4,$y4,$xx4,$yy4,$green);
$data.=$im->gifanimadd(0,0,0,1);
$teller = 0;
again:
for($x=PI/4;$x<=PI/2;$x+=PI/8){
$img = new GD::Image(800,800);
$black = $img->colorAllocate(0,0,0);
$green=$img->colorAllocate(0,255,0);
$white=$img->colorAllocate(0,0,0);
$img->setThickness(3);
@een=(360,360,80);
@twee=(440,360,80);
@drie=(440,360,0);
@vier=(360,360,0);
$straal = sqrt((40*40)+(40*40));
$yh = $straal * sin($x);
$hoogte =$yh-40;
$xv = sqrt($straal**2-$yh**2);
$xver = 40 - $xv;
$een[0]+=$xver;
$een[2]+=$hoogte;
$twee[0]+=$hoogte;
$twee[2]-=$xver;
$drie[0]-=$xver;
$drie[2]-=$hoogte;
$vier[0]-=$hoogte;
$vier[2]+=$xver;
if($een[2]>0){
$x1 =$een[0] + sqrt($een[2]**2/2);
$y1=$een[1] - sqrt($een[2]**2/2);}
else{
$x1 =$een[0] - sqrt($een[2]**2/2);
$y1=$een[1] + sqrt($een[2]**2/2);}
if($twee[2]>0){
$x2 =$twee[0] + sqrt($twee[2]**2/2);
$y2=$twee[1] - sqrt($twee[2]**2/2);}
else{
$x2 =$twee[0] - sqrt($twee[2]**2/2);
$y2=$twee[1] + sqrt($twee[2]**2/2);}
if($drie[2]>0){
$x3 =$drie[0] + sqrt($drie[2]**2/2);
$y3=$drie[1] - sqrt($drie[2]**2/2);}
else{
$x3 =$drie[0] - sqrt($drie[2]**2/2);
$y3=$drie[1] + sqrt($drie[2]**2/2);}
if($vier[2]>0){
$x4 =$vier[0] + sqrt($vier[2]**2/2);
$y4=$vier[1] - sqrt($vier[2]**2/2);}
else{
$x4 =$vier[0] - sqrt($vier[2]**2/2);
$y4=$vier[1] + sqrt($vier[2]**2/2);}
$xx1=$x1;
$xx2=$x2;
$xx3=$x3;
$xx4=$x4;
$yy1=$y1+80;
$yy2=$y2+80;
$yy3=$y3+80;
$yy4=$y4+80;
$img->line($x1,$y1,$x2,$y2,$green);
$img->line($x2,$y2,$x3,$y3,$green);
$img->line($x3,$y3,$x4,$y4,$green);
$img->line($x4,$y4,$x1,$y1,$green);
$img->line($xx1,$yy1,$xx2,$yy2,$green);
$img->line($xx2,$yy2,$xx3,$yy3,$green);
$img->line($xx3,$yy3,$xx4,$yy4,$green);
$img->line($xx4,$yy4,$xx1,$yy1,$green);
$img->line($x1,$y1,$xx1,$yy1,$green);
$img->line($x2,$y2,$xx2,$yy2,$green);
$img->line($x3,$y3,$xx3,$yy3,$green);
$img->line($x4,$y4,$xx4,$yy4,$green);
$data.=$img->gifanimadd(0,0,0,1);
}
$img = new GD::Image(800,800);
$black = $img->colorAllocate(0,0,0);
$green=$img->colorAllocate(0,255,0);
$white=$img->colorAllocate(0,0,0);
$img->setThickness(3);
@een=(360,360,80);
@twee=(440,360,80);
@drie=(440,360,0);
@vier=(360,360,0);
$yh = $straal * sin((PI/8)*5);
$hoogte =$yh-40;
$xv = sqrt($straal**2-$yh**2);
$xver = 40 + $xv;
$een[0]+=$xver;
$een[2]+=$hoogte;
$twee[0]+=$hoogte;
$twee[2]-=$xver;
$drie[0]-=$xver;
$drie[2]-=$hoogte;
$vier[0]-=$hoogte;
$vier[2]+=$xver;
if($een[2]>0){
$x1 =$een[0] + sqrt($een[2]**2/2);
$y1=$een[1] - sqrt($een[2]**2/2);}
else{
$x1 =$een[0] - sqrt($een[2]**2/2);
$y1=$een[1] + sqrt($een[2]**2/2);}
if($twee[2]>0){
$x2 =$twee[0] + sqrt($twee[2]**2/2);
$y2=$twee[1] - sqrt($twee[2]**2/2);}
else{
$x2 =$twee[0] - sqrt($twee[2]**2/2);
$y2=$twee[1] + sqrt($twee[2]**2/2);}
if($drie[2]>0){
$x3 =$drie[0] + sqrt($drie[2]**2/2);
$y3=$drie[1] - sqrt($drie[2]**2/2);}
else{
$x3 =$drie[0] - sqrt($drie[2]**2/2);
$y3=$drie[1] + sqrt($drie[2]**2/2);}
if($vier[2]>0){
$x4 =$vier[0] + sqrt($vier[2]**2/2);
$y4=$vier[1] - sqrt($vier[2]**2/2);}
else{
$x4 =$vier[0] - sqrt($vier[2]**2/2);
$y4=$vier[1] + sqrt($vier[2]**2/2);}
$xx1=$x1;
$xx2=$x2;
$xx3=$x3;
$xx4=$x4;
$yy1=$y1+80;
$yy2=$y2+80;
$yy3=$y3+80;
$yy4=$y4+80;
$img->line($x1,$y1,$x2,$y2,$green);
$img->line($x2,$y2,$x3,$y3,$green);
$img->line($x3,$y3,$x4,$y4,$green);
$img->line($x4,$y4,$x1,$y1,$green);
$img->line($xx1,$yy1,$xx2,$yy2,$green);
$img->line($xx2,$yy2,$xx3,$yy3,$green);
$img->line($xx3,$yy3,$xx4,$yy4,$green);
$img->line($xx4,$yy4,$xx1,$yy1,$green);
$img->line($x1,$y1,$xx1,$yy1,$green);
$img->line($x2,$y2,$xx2,$yy2,$green);
$img->line($x3,$y3,$xx3,$yy3,$green);
$img->line($x4,$y4,$xx4,$yy4,$green);
$data.=$img->gifanimadd(0,0,0,1);
if($teller<20){
$teller++;
goto again;}


$data.=$im->gifanimend;
binmode STDOUT;
print $data;
[download]

have a good day