Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:185AA GHM

Order: 20

Horizontal side: 185 Vertical side: 185

Elements: 5, 5√2, 16√2, 18√2, 32, 35, 30√2, 32√2, 46, 35√2, 50, 39√2, 64, 65, 70, 50√2, 71, 57√2, 100, 75√2.

Code: 752 75 110 574 57 128 390 114 185 711 185 185 186 57 128 467 75 146 166 105 130 327 121 146 320 153 146 300 105 130 641 185 114 56 70 105 703 70 35 55 70 100 657 70 100 1003 135 0 502 185 50 503 185 0 355 0 0 354 35 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)