Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:102AS GHM

Order: 20

Horizontal side: 102 Vertical side: 102

Elements: 3, 3√2, 6, 5√2, 9, 10, 9√2, 10√2, 11√2, 18, 16√2, 18√2, 32, 36, 27√2, 32√2, 33√2, 48, 54, 51√2.

Code: 545 0 48 514 51 51 363 102 66 96 57 57 185 66 48 184 84 48 336 69 33 63 57 51 95 57 48 34 54 48 33 57 48 485 0 0 324 32 16 323 64 16 105 64 38 104 74 38 112 75 27 54 69 33 270 75 27 164 48 0

The properties below may precede order:side in a tiling's title:

• c = crossed. There is a tile-corner traversed by two lines. The only known crossed PPIRTS's below order 20 are 19:35AB1of4 and 19:35AB4of4.
• d = double-pentagon patterned. Every such tiling is a subdivision of an instance of the same deformable tiling by two 45-90-90-90-225 pentagons with a shared side, four triangles and two pseudotriangles. All below order 19 are degenerate in the sense that one or more sides of underlying tiles have shrunk to zero length. The non-degenerate d-tilings of order 19 are 19:221AA, 19:229AB and 19:241AA.
• e = elegant. No tile-corner is just a T-junction. Such tilings may be considered aesthetically pleasing. The only known elegant PPIRTS's below order 16 are 13:21AA, 14:26AJ, 14:35AA and 15:55AA.
• i = isomers exist which are ineligible for this catalogue. They are not included in the isomer count which follows 'of' in the tiling id.
• r = rectangular inclusion. The only known PPIRTS's below order 16 with a rectangular inclusion are 13:18AA1-4of4 and 15:44AA1-4of4.

Credit for Discovery

Just three people are credited with the discovery of Primitive Perfects:

Geoffrey H. Morley (GHM, England)

Jasper D. Skinner, II (JDS, United States)

William T. Tutte (WTT, Canada, 1917-2002) (15:44AI, 17:136AJ and 19:56AJ only)