Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:218AB GHM

Order: 20

Horizontal side: 218 Vertical side: 218

Elements: 7, 12√2, 15√2, 24, 18√2, 30, 24√2, 34, 36, 41, 33√2, 34√2, 41√2, 68, 75, 68√2, 102, 109, 116, 109√2.

Code: 1167 0 218 680 116 218 681 184 218 342 218 184 341 218 218 753 218 109 156 33 135 307 48 150 126 66 138 247 78 150 246 78 126 415 102 109 414 143 109 186 48 120 365 66 102 330 33 135 77 102 109 1090 109 109 1091 218 109 1027 0 102

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)