The agnicayana's central act is architectural. Over its twelve days, and after long preliminary rites, the priests and their helpers lay out and construct an altar of more than a thousand kiln-fired bricks, each with its own name, its own dedicatory formula and its own appointed place, in five layers whose plan is a syena, a falcon or eagle with wings spread in flight.
The brahmana texts explain the shape: Prajapati, the creator, exhausted and dismembered himself in creating the world, and the piling of the altar puts him together again, while the bird form is the sacrifice itself taking wing to carry the sacrificer to heaven. The geometry is not decorative. The altar must occupy a prescribed area regardless of its shape, and successive performances required constructions for transforming shapes while preserving area, problems whose solutions are recorded in the Shulba Sutras, the ritual geometry handbooks that are the oldest mathematical texts of India and contain, centuries before Pythagoras' name attached to it, a general statement of the relation between the sides of a right triangle. Above the bricklaying runs the full apparatus of a great soma rite: continuous recitation from three Vedas, the pressing and offering of soma, the animal offerings of the classical prescriptions, and the final installation of the fire on the completed altar, at which point the whole edifice, weeks of labour and three millennia of transmission, has served its purpose and is abandoned to the elements.