using System;

using System.Collections.Generic;

using System.Numerics;

public class Program

{

    public static void Main()

    {

        Traversal t = new Traversal(0, 5);

        List<Vector2> points = new List<Vector2>();

        t.Traverse(1);

        t.Traverse(4);

        Console.WriteLine(t.CartesianPoint());

        /*

        for (int i = 1; i <= 5; i++)

        {

            Traversal tt = new Traversal(0, 5);

            tt.Traverse(i);

            for (int j = 1; j <= 5; j++)

            {

                tt.Traverse(j);

                points.Add(tt.CartesianPoint());

                tt.RemoveLast();

            }

            tt.RemoveLast();

        }*/

        Traversal tt = null;

        Iteration(tt, 0, points);

        foreach(Vector2 p in points)

        {

            Console.WriteLine(p.X + ", " + p.Y);

        }

    }

    public static void Iteration(Traversal t, int depth, List<Vector2> points)

    {

        if (depth == 0)

        {

            points.Add(new Traversal(0,5).CartesianPoint());

            return;

        }

        Iterate(t, depth, depth, points);

    }

    public static void Iterate(Traversal t, int startDepth, int depth, List<Vector2> points)

    {

        if (depth <= 0)

        {

            points.Add(t.CartesianPoint());

            return;

        }

        for (int i = 1; i <= 5; i++)

        {

            if (startDepth == depth)

            {

                t = new Traversal(0, 5);

            }

            t.Traverse(i);

            Iterate(t, startDepth, depth - 1, points);

            t.RemoveLast();

        }

    }

}

​

public class Traversal

{

    public float sideLength = 1;

    public float apothem;

    public float theta;

    public int startRotation;

    public int polySides;

    public List<int> sideNumbers = new List<int>();

    public Traversal(int startRotation, int polySides)

    {

        this.startRotation = startRotation;

        this.polySides = polySides;

        apothem = (float)(sideLength / (2 * Math.Tan(DegToRad(180.0f / polySides))));

        theta = 360.0f / polySides;

    }

    public void Traverse(int side)

    {

        if (side <= 5 && side > 0)

        {

            sideNumbers.Add(side);

        }

    }

    public void RemoveLast()

    {

        sideNumbers.RemoveAt(sideNumbers.Count - 1);

    }

    public Vector2 CartesianPoint()

    {

        int rot = startRotation;

        float x = 0;

        float y = 0;

        for (int i = 0; i < sideNumbers.Count; i++)

        {

            x += (1 - 2 * rot) * (2 * apothem * (float)Math.Sin(DegToRad(theta * sideNumbers[i] - theta / 2.0f)));

            y += (1 - 2 * rot) * (2 * apothem * (float)Math.Cos(DegToRad(theta * sideNumbers[i] - theta / 2.0f)));

            rot = 1 - rot;

        }

        x = (float)Math.Round(x, 4);

        y = (float)Math.Round(y, 4);

        return new Vector2(x,y);

    }

    public static float DegToRad(float degrees)

    {

        return degrees * (float)(Math.PI/180.0f);

    }

}