Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:340AZ GHM

Order: 20

Horizontal side: 340 Vertical side: 340

Elements: 5, 5√2, 10, 10√2, 15√2, 35, 27√2, 50, 54, 62, 54√2, 56√2, 58√2, 108, 112, 120, 114√2, 120√2, 220, 170√2.

Code: 2205 0 120 1704 170 170 1146 226 226 560 226 226 501 220 170 355 220 135 621 282 170 582 340 112 57 220 135 50 225 135 154 240 120 270 255 135 107 220 130 100 230 130 1205 0 0 1204 120 0 1123 340 0 1083 228 0 542 282 54 541 282 108

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)