Aside from the importance of entrance from the east, the eastern direction is replete with symbolisms, and the Agnihotra is no exception in its explications to that effect:
Approaching betweent eh Gaarhapatya and the Aahavaniiya, the east here is likened with heaven.
. includes the section on the Gaayatrii mentioned
, the significations of the Aahavaniiya with the sky, and that of the Gaarhapatya with the earth, etc.