Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:291AB GHM

Order: 20

Horizontal side: 291 Vertical side: 291

Elements: 8√2, 16, 16√2, 30, 32, 37, 40, 30√2, 53, 40√2, 60, 80, 60√2, 90, 111, 120, 90√2, 150, 111√2, 201.

Code: 2017 0 291 600 201 291 601 261 291 302 291 261 301 291 291 1503 291 111 803 141 151 1207 141 231 80 61 151 404 101 111 403 141 111 533 53 90 167 53 143 166 53 127 325 69 111 375 53 90 1114 180 0 1113 291 0 907 0 90 900 90 90

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)