Is it permissible for a Catholic to pray the Salat? I'm thinking of visiting a mosque on Wednesday. I've done this before a couple of years ago and it was a very valuable experience. The last time I visited I joined in the Salat and thought it was a great way to pray.

I've since wondered whether it is actually ok to pray the Salat. I don't think there is anything heretical about the movements; I find them quite beautiful and I believe that they are worshipping the true God. However I have reservations about the fact that the Salat is prayed towards the Kaabah in Mecca. 

If it was prayed towards a tabernacle, a Eucharistic host, liturgical east, or no particular direction at all then I wouldn't have any problems with it. But because it is prayed towards a stone box in Saudi Arabia I worry that the whole thing might be a form of idolatry.

What is the Catholic view of this situation? Two main questions:


Is it permissible to pray the Salat while facing Mecca? 
Is it permissible to pray the Salat while facing a Eucharistic host, a tabernacle, liturgical east, or nowhere in particular?


Note that for the purposes of this question I'm considering Allah and Yahweh to be the same God, as per dogmatic constitution Lumen Gentium and the CCC paragraph 841. Any answer which disagrees is out of scope and will be downvoted
No, it is forbidden for Catholics to engage in communicatio in sacris (joining others in false worship, e.g., worshipping Islam's false god Allah, who is not the Holy Trinity):


  1917 Canon 1258 §1 It is not licit for the faithful by any manner to assist actively or to have a part in the sacred [rites] of non-Catholics.


cf. Dom Augustine's A Commentary on the New Code of Canon Law on '17 Can. 1258

This law is expressed in the 1983 code, in the section "Delicts against religion and the unity of the Church," as:


  1983 Can. 1365 A person guilty of prohibited participation in sacred rites (communicatio in sacris) is to be punished with a just penalty.


cf. this commentary on '83 Can. 1365