Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:254AR GHM

Order: 20

Horizontal side: 254 Vertical side: 254

Elements: 1√2, 20, 20√2, 35, 37, 40, 42, 36√2, 42√2, 64, 72, 84, 72√2, 73√2, 104, 74√2, 106, 75√2, 108, 106√2.

Code: 1087 0 254 726 36 182 1047 108 254 843 212 170 422 254 212 421 254 254 1066 148 106 366 0 146 725 36 110 200 128 170 201 148 170 647 148 170 407 108 150 756 73 75 732 73 73 371 73 110 357 73 110 1065 148 0 12 74 74 740 74 74

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)