Bernini designed the Altar of the Chair in the Vatican Basilica to be seen and used like this...
...celebrant and people pray together facing the great relic under the protection of the Holy Ghost. (Image: Schola Sainte-Cécile, Sat. Oct. 26, 2013)
|St. Pius X celebrates Mass at the Altar of the Chair, 1906|
Only 49 years ago - therefore, already in the aftermath of Sacrosanctum Concilium, Paul VI was still using it facing the liturgical East (incidentally, geographical West), using the original altar mensa, destroyed in the 1990s:
|Consecration of Bishops, 1964|
The current stand-alone structure is the second one since the Council, installed under Benedict XVI, a considerable improvement on the anvil-like monstrosity installed by Cardinal Noè when the original altar was annihilated (cf. our 2006 post on this).