Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:270AJ GHM

Order: 20

Horizontal side: 270 Vertical side: 270

Elements: 9√2, 14, 23√2, 38, 46, 38√2, 58, 60, 46√2, 69, 76, 58√2, 60√2, 87, 96, 76√2, 116, 87√2, 96√2, 116√2.

Code: 1165 0 154 1164 116 154 380 232 270 381 270 270 760 194 232 761 270 232 600 118 156 601 178 156 465 178 110 464 224 110 693 270 87 585 0 96 584 58 96 145 178 96 234 201 87 965 0 0 964 96 0 90 192 96 870 183 87 871 270 87

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)