A number of archaic altars shapes existed for the agnichayana of which the practical geometric knowledge is largely lost in the surviving shrauta tradition.
The most famous which are still performed are: 1) the broad winged ShaDpatrika shyenachiti or the gliding eagle altar with 6 feathered wings. There is a variant of this with wings entirely made of 6 rows of parallelogram bricks.
2) the drawn wing pa~Nchapatrika shyenachiti or the diving eagle altar with 5 feathered wings.
3) The pIthachiti- In the form a square with 3 rectangular paths leading out on 3 of the sides (this is nearly extinct, only a single Andhra ritualist, whose patnI is also a qualified soma ritualist, knows this.
4) The puruShachiti- in the form of a standing man with arms extended to the sides.
5) The kUrmachiti- in the form of a turtle
The less known ones:
6) The ka~nkachiti- in the form of a flying heron
7) The alajachiti- in the form of an alaja bird with four furrow like paths leading out in the cardinal directions.
8) praugachiti- in the form of an equilateral triangle
9) droNachiti- in the form of a droNa kalasha
10) rathachakrachiti- in the form of a spoked wheel
11) parichAyyaM- a circular altar
12) shmashAnachiti- in the form resembling a tomb (shmashAna described in the yajurvedic burial rite for the bones of a dead clansman)
All the altars have 5 layers of bricks.