Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:89AD GHM

Order: 20

Horizontal side: 89 Vertical side: 89

Elements: 1, 1√2, 2, 3, 12√2, 13√2, 14√2, 20, 15√2, 23, 28, 20√2, 29, 30, 23√2, 26√2, 40, 30√2, 46, 33√2.

Code: 332 33 56 304 30 59 303 60 59 152 75 74 291 89 89 283 75 46 142 89 60 403 89 20 31 33 59 17 33 59 10 34 59 134 47 46 27 33 58 120 35 58 236 0 23 465 23 0 264 49 20 235 0 0 204 69 0 203 89 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)