Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:340AT GHM

Order: 20

Horizontal side: 340 Vertical side: 340

Elements: 18, 18√2, 30, 36, 29√2, 30√2, 36√2, 58, 60, 47√2, 58√2, 60√2, 94, 69√2, 90√2, 94√2, 152, 188, 141√2, 152√2.

Code: 1887 0 340 1520 188 340 1521 340 340 366 0 152 307 36 188 300 66 188 904 156 98 476 199 141 947 246 188 946 246 94 607 36 158 600 96 158 365 0 116 1410 199 141 582 58 58 184 18 98 183 36 98 694 87 29 583 58 0 292 87 29

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)