Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:187AB GHM

Order: 20

Horizontal side: 187 Vertical side: 187

Elements: 2, 7, 7√2, 14, 21, 21√2, 35, 37, 42, 36√2, 37√2, 38√2, 70, 72, 74, 75, 76, 77, 75√2, 76√2.

Code: 765 0 111 764 76 111 423 152 145 212 173 166 351 187 187 213 173 145 145 173 152 75 173 145 74 180 145 773 187 75 723 110 73 707 110 145 745 0 37 384 38 73 27 110 75 750 112 75 751 187 75 364 74 37 375 0 0 374 37 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)