Careful, square six with firebricks might not leave much space for insulation.
Did the maths. Across, it's 38 cm without insulation .
Plus insulation, you
should be around 44 across.
Inside of a barrel is around 59/60cm
That should be all right.
As for material list. I dont think there is one.
You need about 45 bricks for the riser.
May be as much for the batch. Half a roll of
superwool. 1/2 inch . metal for the door and holding the bricks. The solution is drawing and planning.