Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:234AS GHM

Order: 20

Horizontal side: 234 Vertical side: 234

Elements: 6, 6√2, 7√2, 22√2, 36, 29√2, 30√2, 44, 48, 36√2, 54, 58, 44√2, 48√2, 88, 95, 102, 132, 95√2, 139.

Code: 1395 0 95 1321 132 234 482 180 186 1021 234 234 483 180 138 545 180 132 367 132 138 360 168 138 64 174 132 63 180 132 304 204 102 883 234 44 74 139 95 296 117 73 587 146 102 957 0 95 950 95 95 224 117 73 444 190 0 443 234 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)