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Interior chimneys are at least 4" larger in all four directions than the flue they contain. A chimney containing a 12"x12" clay flue liner must be at least 20" by 20". Combustible materials must be kept at least 2" away from the outside of the chimney walls. Exterior chimneys only need to be 1" away from the exterior combustible wall of the house.
By code the chimney must extend at least three feet above the roof and two feet above any part of the roof within ten feet. Cast in place or use a pre-cast concrete chimney cap with a drip edge and caulk the joint between the cap and the top flue liner with a silicon sealant.
In Seismic areas place a #4 steel reinforcing bar in each corner of the chimney, preferrably in the cells of the brick or block, and grout solid. If you must place the reinforcing steel between the flue liner and the surrounding masonry we recommend wrapping the flues with 1/8" ceramic fiber paper "socks" before placing the grout to allow the flue liners a lttle room to expand without cracking the exterior masonry. Tie the surrounding masonry horizontally every 18" with steel ladder or K-web, or pencil rod in the bed joints. Exterior chimneys must be anchored at each floor and roof.
The surround (the area at least 6" wide around the fireplace opening) can be finished with brick, stone, tile, terra cotta, slate, marble - almost any decorative masonry material. 100 years ago fireplace surrounds were often finished with ordinary plaster and sometimes painted black. The surround should not be used to lower the opening of the fireplace. The part of the surround over the fireplace opening should be just low enough to cover the edge of the rounded Rumford throat and not so low that it might cause unwanted turbulence.
I have Rumford fireplaces in my antique house. When we had an addition built in 1998 we added another one. My advice would be to fine an experienced mason who has built these before and check with the local building department to be sure it can be done with all the building code requirements in place today. If I had it to do over I would have tried to get “pumpkin seed” brick. It is an antique English brick, a little smaller with a narrower face compared to new brick, which came over from England as ballast in the ships.