Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:102AI4of4 GHM

Order: 20

Horizontal side: 102 Vertical side: 102

Elements: 3√2, 6, 8, 8√2, 14, 16, 14√2, 22, 16√2, 24, 28, 22√2, 24√2, 36, 28√2, 30√2, 44, 33√2, 36√2, 44√2.

Code: 445 0 58 444 44 58 140 88 102 141 102 102 280 74 88 281 102 88 243 46 36 87 46 60 80 54 60 244 78 36 306 72 30 225 0 36 224 22 36 167 46 52 160 62 52 365 0 0 364 36 0 36 69 33 67 72 36 330 69 33

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)