A method of machining a combustion chamber roof surface in a cylinder head for a lean-burn gasoline engine, wherein the machined cylinder head comprises: a substantially planar gasket interface surface; and a combustion chamber extending into the cylinder head away from the gasket interface surface, wherein the combustion chamber roof surface intersects the gasket interface surface to define a combustion chamber opening, the method comprising: using a first cutter to machine a first pair of facets (181, 182) of the combustion chamber roof surface, wherein a first one of the first pair of facets is located at least partially between a pair of air inlet openings in the combustion chamber roof located on an air inlet side of the combustion chamber, and a second one of the first pair of facets is located at least partially between a pair of exhaust outlet openings in the combustion chamber roof located on an exhaust outlet side of the combustion chamber; using a second cutter to machine a second pair of facets (185a, 185b) of the combustion chamber roof surface, wherein the second pair of facets are located between the pair of air inlet openings and the pair of exhaust outlet openings such that each one of the second pair of facets extends between the air inlet side of the combustion chamber and the exhaust outlet side of the combustion chamber; and using the second cutter to machine a third pair of facets (186a, 186b) of the combustion chamber roof surface, wherein a first one of the third pair of facets is located between a first one of the air inlet openings and a first one of the exhaust outlet openings, and a second one of the third pair of facets is located between a second one of the air inlet openings and a second one of the exhaust outlet openings. a substantially planar gasket interface surface; and a combustion chamber extending into the cylinder head away from the gasket interface surface, wherein the combustion chamber roof surface intersects the gasket interface surface to define a combustion chamber opening, the method comprising: using a first cutter to machine a first pair of facets (181, 182) of the combustion chamber roof surface, wherein a first one of the first pair of facets is located at least partially between a pair of air inlet openings in the combustion chamber roof located on an air inlet side of the combustion chamber, and a second one of the first pair of facets is located at least partially between a pair of exhaust outlet openings in the combustion chamber roof located on an exhaust outlet side of the combustion chamber; using a second cutter to machine a second pair of facets (185a, 185b) of the combustion chamber roof surface, wherein the second pair of facets are located between the pair of air inlet openings and the pair of exhaust outlet openings such that each one of the second pair of facets extends between the air inlet side of the combustion chamber and the exhaust outlet side of the combustion chamber; and using the second cutter to machine a third pair of facets (186a, 186b) of the combustion chamber roof surface, wherein a first one of the third pair of facets is located between a first one of the air inlet openings and a first one of the exhaust outlet openings, and a second one of the third pair of facets is located between a second one of the air inlet openings and a second one of the exhaust outlet openings. using a first cutter to machine a first pair of facets (181, 182) of the combustion chamber roof surface, wherein a first one of the first pair of facets is located at least partially between a pair of air inlet openings in the combustion chamber roof located on an air inlet side of the combustion chamber, and a second one of the first pair of facets is located at least partially between a pair of exhaust outlet openings in the combustion chamber roof located on an exhaust outlet side of the combustion chamber; using a second cutter to machine a second pair of facets (185a, 185b) of the combustion chamber roof surface, wherein the second pair of facets are located between the pair of air inlet openings and the pair of exhaust outlet openings such that each one of the second pair of facets extends between the air inlet side of the combustion chamber and the exhaust outlet side of the combustion chamber; and using the second cutter to machine a third pair of facets (186a, 186b) of the combustion chamber roof surface, wherein a first one of the third pair of facets is located between a first one of the air inlet openings and a first one of the exhaust outlet openings, and a second one of the third pair of facets is located between a second one of the air inlet openings and a second one of the exhaust outlet openings.