Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:270AS GHM

Order: 20

Horizontal side: 270 Vertical side: 270

Elements: 10√2, 20, 15√2, 20√2, 30, 40, 34√2, 60, 64, 66, 68, 70, 66√2, 68√2, 70√2, 100, 85√2, 134, 136, 170.

Code: 1705 0 100 1361 136 270 682 204 202 1341 270 270 683 204 134 662 270 136 663 270 70 344 170 100 643 204 70 1005 0 0 854 85 15 403 140 30 607 140 70 700 200 70 701 270 70 156 85 15 305 100 0 204 120 10 203 140 10 104 130 0

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)