Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:218AA GHM

Order: 20

Horizontal side: 218 Vertical side: 218

Elements: 6, 7, 24, 18√2, 30, 22√2, 24√2, 36, 29√2, 44, 48, 51, 58, 72, 51√2, 58√2, 102, 80√2, 116, 109√2.

Code: 1165 0 102 1094 109 109 806 138 138 290 138 138 71 116 109 517 116 109 510 167 109 1025 0 0 721 72 102 485 72 54 441 116 102 224 138 36 580 160 58 581 218 58 245 72 30 244 96 30 180 120 54 63 102 30 367 102 36 301 102 30

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)