３角形から８角形までを生成する最低限のコード

CreateLine

[RequireComponent(typeof(LineRenderer))]
public class Test : MonoBehaviour
{
    [SerializeField]
    [Range(0, 5)]
    private int _index = 0;

    private static readonly int[] PointsNumbers = { 3, 4, 5, 6, 7, 8 };

    private LineRenderer _lineRenderer = null;

    private void Awake()
    {
        CreateLine();
    }

    private void CreateLine()
    {
        int initiatorPointsAmount = PointsNumbers[_index];

        Vector3 rotateVector = new Vector3(1.0f, 0.0f, 0.0f);

        Vector3[] sourcePositions = new Vector3[initiatorPointsAmount + 1];

        for (var i = 0; i < initiatorPointsAmount; i++)
        {
            sourcePositions[i] = rotateVector;
            rotateVector = Quaternion.AngleAxis(360.0f / initiatorPointsAmount, new Vector3(0.0f, 0.0f, 1.0f)) * rotateVector;
        }

        sourcePositions[initiatorPointsAmount] = sourcePositions[0];

        if (TryGetComponent<LineRenderer>(out _lineRenderer))
        {
            _lineRenderer.enabled = true;
            _lineRenderer.useWorldSpace = false;
            _lineRenderer.loop = true;
            _lineRenderer.positionCount = sourcePositions.Length;
            _lineRenderer.SetPositions(sourcePositions);
        }
    }
}