Pentagramm

package com.example.foo;

import java.awt.BorderLayout;
import java.awt.Graphics;
import java.awt.Polygon;
import java.awt.event.WindowAdapter;
import java.awt.event.WindowEvent;
import java.awt.event.WindowListener;
import java.util.Arrays;

import javax.swing.JDialog;
import javax.swing.JPanel;
import javax.swing.SwingUtilities;
import javax.swing.WindowConstants;

public class SomeClass {

  public static void main(String[] args) {
    SwingUtilities.invokeLater(SomeClass::main2);
  }

  static void main2() {
    JDialog dlg = new JDialog();
    dlg.setSize(400, 400);
    JPanel pnl = new JPanel() {
      private static final long serialVersionUID = -8457824227977035142L;

      public void paint(Graphics g) {
        super.paint(g);
        g.drawPolygon(star(200));
      };
    };
    pnl.setSize(400, 400);
    dlg.getRootPane().setLayout(new BorderLayout());
    dlg.getRootPane().add(pnl);
    dlg.setDefaultCloseOperation(WindowConstants.DISPOSE_ON_CLOSE);
    dlg.addWindowListener(new WindowAdapter() {
      @Override
      public void windowClosed(WindowEvent e) {
        System.exit(0);
      }
    });
    dlg.setVisible(true);
  }

  static Polygon star(final int r) {
    final int n = 5;
    final double angle = 2d * Math.PI / n;
    final double side = 2d * r * Math.cos(angle);
    int[] xs = new int[n];
    int[] ys = new int[n];
    double x = r;
    double y = 0;
    double φ = angle;
    for (int ω = 0; ω < n * 2; ω += 2) {
      final int i = ω % n;
      xs[i] = (int) x;
      ys[i] = (int) y;
      x += (side * Math.cos(φ));
      y += (side * Math.sin(φ));
      φ += angle;
    }
    return new Polygon(xs, ys, n);
  }
}