Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:187AF GHM

Order: 20

Horizontal side: 187 Vertical side: 187

Elements: 2, 3√2, 6, 8, 6√2, 10, 8√2, 12, 10√2, 14√2, 25, 28, 28√2, 53, 53√2, 78, 67√2, 106, 81√2, 134.

Code: 1347 0 187 1063 134 81 532 187 134 531 187 187 676 120 67 286 0 53 787 28 81 810 106 81 144 120 67 285 0 25 255 0 0 104 10 15 103 20 15 87 20 25 86 20 17 25 20 15 121 22 15 62 28 9 63 28 3 34 25 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)