Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:190AM GHM

Order: 20

Horizontal side: 190 Vertical side: 190

Elements: 11, 14, 11√2, 12√2, 22, 24, 33, 38, 31√2, 33√2, 48, 52, 38√2, 48√2, 52√2, 76, 83, 71√2, 107, 76√2.

Code: 1075 0 83 764 76 114 763 152 114 382 190 152 381 190 190 526 138 100 314 107 83 336 105 81 147 138 114 525 138 48 837 0 83 126 71 71 247 83 83 223 105 59 335 105 48 710 71 71 114 94 48 113 105 48 484 142 0 483 190 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)