Constantine’s Prayer Tent

In my reading I came across a reference to a prayer Tabernacle or tent set up by the Emperor Constantine on his campaigns. I wondered if it was based on the Tabernacle of Moses and what it looked like? A couple citations about the Tabernacle are:

So great indeed was the emperor’s devotion to Christianity, that when he was about to enter on a war with Persia, he prepared a tabernacle formed of embroidered linen on the model of a church, just as Moses had done in the wilderness; and this so constructed as to be adapted to conveyance from place to place, in order that he might have a house of prayer even in the most desert regions.

Socrates, Ecclesiastical History, Book I, Chapter XVIII.

When he engaged in war, he caused a tent to be borne before him, constructed in the shape of a church, so that in case he or his army might be led into the desert, they might have a sacred edifice in which to praise and worship God, and participate in the mysteries. Priests and deacons followed the tent, who fulfilled the orders about these matters, according to the law of the church. From that period the Roman legions, which now were called by their number, provided each its own tent, with attendant priests and deacons.

Sozomenus, Ecclesiastical History, Book I, Chapter VIII

It seems that the model was indeed the Mosaic Tabernacle as far as materials go, however, in the shape of the cross and containing the Christian liturgy. I’d love to learn more about this tent, but I don’t know if there is more source material.