Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:172AP1of4 GHM

Order: 19

Horizontal side: 172 Vertical side: 172

Elements: 6√2, 12, 12√2, 21, 24, 18√2, 26, 21√2, 36, 26√2, 42, 47, 52, 73, 52√2, 78, 94, 99, 73√2.

Code: 995 0 73 781 78 172 182 96 154 941 172 172 126 84 142 245 96 130 66 78 136 125 84 130 425 78 94 361 120 130 522 172 78 214 99 73 213 120 73 523 172 26 737 0 73 730 73 73 471 120 73 264 146 0 263 172 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)