Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:264AX GHM

Order: 20

Horizontal side: 264 Vertical side: 264

Elements: 4, 4√2, 14, 14√2, 15√2, 28, 30, 26√2, 38, 28√2, 34√2, 38√2, 68, 64√2, 68√2, 98, 83√2, 98√2, 166, 132√2.

Code: 1665 0 98 1324 132 132 646 200 200 683 200 132 382 238 162 383 238 124 262 264 136 686 196 68 344 166 98 46 196 128 303 196 98 45 196 124 282 224 96 281 224 124 142 238 110 141 238 124 985 0 0 984 98 0 156 181 83 830 181 83

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)