Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:234AP GHM

Order: 20

Horizontal side: 234 Vertical side: 234

Elements: 12, 12√2, 21, 24, 25, 18√2, 25√2, 36, 46, 50, 36√2, 54, 46√2, 71, 84, 92, 96, 117, 138, 117√2.

Code: 1385 0 96 1174 117 117 1173 234 117 211 138 117 257 138 117 250 163 117 711 234 117 965 0 0 841 84 96 362 120 60 541 138 96 507 138 92 923 188 0 462 234 46 363 120 24 182 138 42 463 234 0 127 84 24 126 84 12 247 96 24

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)