Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:157AD GHM

Order: 20

Horizontal side: 157 Vertical side: 157

Elements: 7, 5√2, 8, 8√2, 15, 11√2, 16, 12√2, 22, 23, 17√2, 22√2, 34, 45, 34√2, 45√2, 56√2, 90, 67√2, 112.

Code: 1127 0 157 903 112 67 452 157 112 451 157 157 566 101 56 226 0 45 345 22 33 344 56 33 670 90 67 114 101 56 225 0 23 52 27 28 174 39 16 120 27 28 235 0 0 151 15 23 77 15 23 87 15 16 86 15 8 167 23 16

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)