from Google Maps
The Chapel was physically built between the Church and the Palace upon the King's decision. The Shroud is placed inside a private chapel, but is accessible to the public via the metropolitan church. The architecture is the physical mirror of what the Shroud symbolically represented: the divine legitimation of the secular power of the House of Savoy, that owned the proof of the resurrection of Christ.
The picture shows the chapel nestled between the palace and the Dome.