Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:340AH GHM

Order: 20

Horizontal side: 340 Vertical side: 340

Elements: 19√2, 22√2, 44, 58, 44√2, 47√2, 78, 58√2, 88, 69√2, 98, 78√2, 116, 88√2, 126, 136, 98√2, 107√2, 164, 126√2.

Code: 1647 0 340 980 164 340 981 262 340 782 340 262 781 340 340 1363 340 126 220 66 242 694 135 173 1163 204 126 582 262 184 581 262 242 440 44 220 441 88 220 472 135 173 882 88 88 881 88 176 192 107 107 1264 214 0 1263 340 0 1070 107 107

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)