Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:188AK GHM

Order: 20

Horizontal side: 188 Vertical side: 188

Elements: 10, 10√2, 20, 21√2, 30, 32, 23√2, 30√2, 32√2, 46, 50, 39√2, 60, 64, 46√2, 78, 82, 64√2, 69√2, 78√2.

Code: 785 0 110 784 78 110 320 156 188 321 188 188 640 124 156 641 188 156 605 0 50 394 39 71 216 39 71 827 60 92 236 119 69 467 142 92 466 142 46 690 119 69 505 0 0 304 30 20 303 60 20 201 50 20 102 60 10 101 60 20

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)