Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:340AL GHM

Order: 20

Horizontal side: 340 Vertical side: 340

Elements: 5√2, 10, 18√2, 25√2, 36, 50, 36√2, 62, 50√2, 72, 62√2, 88, 98, 100, 80√2, 90√2, 160, 170, 180, 170√2.

Code: 1807 0 340 1003 180 240 627 180 340 620 242 340 981 340 340 887 180 278 186 250 260 367 268 278 360 304 278 900 250 260 721 340 242 800 80 240 504 130 190 503 180 190 254 155 165 56 155 165 107 160 170 1700 170 170 1701 340 170 1607 0 160

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)