Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:160AM GHM

Order: 20

Horizontal side: 160 Vertical side: 160

Elements: 1, 9√2, 18, 19, 14√2, 20, 20√2, 32, 23√2, 36, 28√2, 40, 32√2, 46, 40√2, 41√2, 64, 80, 64√2, 80√2.

Code: 805 0 80 804 80 80 646 96 96 363 96 60 645 96 32 402 40 40 401 40 80 205 40 60 204 60 60 195 40 41 284 68 32 146 82 46 236 59 23 465 82 0 17 40 41 410 41 41 181 59 41 92 68 32 324 128 0 323 160 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)