// Rotates a dodec about a vertex or edge to get a dual dodec. private static Dodec GetDual(Dodec dodec, Vector3D rotationPoint) { //double rot = System.Math.PI / 2; // Edge-centered double rot = 4 * (-Math.Atan((2 + Math.Sqrt(5) - 2 * Math.Sqrt(3 + Math.Sqrt(5))) / Math.Sqrt(3))); // Vertex-centered Mobius m = new Mobius(); if (Infinity.IsInfinite(rotationPoint)) { m.Elliptic(Geometry.Spherical, new Vector3D(), -rot); } else { m.Elliptic(Geometry.Spherical, rotationPoint, rot); } Dodec dual = new Dodec(); foreach (Vector3D v in dodec.Verts) { Vector3D rotated = m.ApplyInfiniteSafe(v); dual.Verts.Add(rotated); } foreach (Vector3D v in dodec.Midpoints) { Vector3D rotated = m.ApplyInfiniteSafe(v); dual.Midpoints.Add(rotated); } return(dual); }