Mathematical Architecture and Mathematical Tiles

68a Kelmscott Road, Wandsworth, SW11, is a modern building by Simon Humphreys, 1998, whose volume is defined by the Fibonacci series.

Marble Hill House, Twickenham, has a main room which is cubical (24 ft cube, if I remember correctly). In one of the upper bedrooms are two lacquered tin canisters in the shape of dodecahedra. They are Pontypool ware, English, 19C, labelled Coffee and Tea.

Sudbrook Park, now the Richmond Golf Club, but actually in Petersham, has a 1726 house designed by James Gibbs with a handsome Cube Room. It is grudgingly open to visitors.

Modern concrete and fabric architecture has produced a number of buildings and structures using three-dimensional saddle Surfaces, usually hyperbolic paraboloids, though cooling towers are usually hyperboloids of revolution of one sheet. These sometimes occur because they are ruled surfaces and hence it is easy to make the forms for the concrete. I think a fabric panel tensioned at the corners, with two alternate corners going upward and the other two other going downward, does form a hyperbolic paraboloid.
According to Ian Nairns book, there are hyperbolic paraboloids at:
William Mallinsons Timber Yard, Parnell Road, Poplar (1961);
The Commonwealth Institute, Kensington High Street (on three supports, which sounds more like a monkey saddle??) (1960-1962);
Two Bishops School, Southwark (a tent shape with four corners turned up) (1959-1960).
It is not always clear if architectural writers have got the correct name for the shapes described.

There are ten known examples of Mathematical Tiles in London.
The Notes of Ewell Symposium describes six examples:
David Garricks villa at Hampton;
Cheam Rectory, 15 Maldon Road, Cheam;
13 Crown Hill, Croydon (where there were many examples in the 19C and nearby 35 Surrey Street may have mathematical tiles);
Queensbury House, 7 Burlington Gardens (where the tiles occur around a roof enclosure);
4 John Street (where the tiles are on a rear bay);
74 Long Lane, Smithfield (where the nearby gate of St Bartholomews Priory had mathematical tiles until restored in the early 20C).
A letter of Mrs Garrick says William Chambers referred to the new tiling now made use of in c1780. Mathematicall tyles were used on Drury Lane Theatre in 1794. Later work extended the number of London examples to ten.