A broach spire is a type of spire (a spire is a tall pyramidal or conical structure, usually on the top of a tower or turret) that starts on a square base and is carried up to a tapering octagonal spire by means of triangular faces.
Cathedral Church of Saint Martin, Leicester
Saint Andrew's Church, Broughton, Northamptonshire
St John's Church, Weston, Runcorn, with its short broach spire
St. Laurence and All Saints Church, Eastwood
St Mary's Church, New Mills, Derbyshire
All Saints, Coddington, Herefordshire