Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:160AS GHM

Order: 20

Horizontal side: 160 Vertical side: 160

Elements: 3√2, 4√2, 6, 8, 6√2, 12, 18, 14√2, 28, 21√2, 36, 42, 36√2, 40√2, 60, 44√2, 72, 80, 88, 80√2.

Code: 885 0 72 804 80 80 803 160 80 81 88 80 365 88 44 364 124 44 406 120 40 725 0 0 601 60 72 425 60 30 281 88 72 144 102 30 440 116 44 44 120 40 185 60 12 214 81 9 121 72 12 62 78 6 61 78 12 32 81 9

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)