
"Lastly the three high towers rising up into the sky will give dramatic contrast to the otherwise horizontal treatment of the buildings and, by their distinctive form and relationship to each other, will both mark the change of axis at ground level and give identity to the neighbourhood from afar."
Chamberlin, Powell & Bon, Architects "Barbican Redevelopment" April 1959
"They have wild and wilful top features and jagged balconies passing between the inner and outer uprights of the external framing."
"The Buildings of England" Nikolaus Pevsner and Simon Bradley
The towers' height (above podium level) is 43 storeys in the case of Cromwell Tower and 44 storeys in the case of Lauderdale and Shakespeare Towers. They look triangular but, strictly speaking, they are polygonal. They are all much the same internally. Leaving aside the penthouses at the top of each tower, each floor houses three flats - one flat to a side, more or less. The three flats themselves are different: there's a type 4A a 4B and a 4C flat. The same type 4A a 4B and 4C flat appears in each tower. So if you knew every inch of the three flats on a floor in Lauderdale Tower and were whisked to a floor in Shakespeare or Cromwell, then (leaving aside furniture) you wouldn't know you had left Lauderdale Tower. The giveaway would be if you looked out of the window, because the axis of each tower is different - the 4A flats in Lauderdale, Cromwell and Shakespeare have quite different views across London.
The towers roughly run along the line of Beech Street and also roughly divide the north from the south Barbican areas. Lauderdale is solidly in the south area. Shakespeare has entrances from the south Barbican podium and the north Barbican podium (effectively a floor up). Cromwell can be accessed from the north Barbican podium and from real street level.
Each tower has three passenger lifts from a central lobby so that the residents have a choice of three lifts, or more importantly there is a reduced risk of being stranded by an out-of-order lift.
The design of the towers underwent changes after the original plan in 1959. An irregular roof line, triangular projecting balconies, and vertical structural members were introduced to the design. Among the buildings which influenced this design was the Price Tower designed by Frank Lloyd Wright in 1953 to 1955 which Peter Chamberlin visited in the early 1960s.

The towers seen from the other side of the Thames on a summer's evening.
The three towers
Victorian factory chimneys
Flat design
Zig-zag drains
Balconies
Service hatches
The towers seen from Smithfield