Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:302AH GHM

Order: 19

Horizontal side: 302 Vertical side: 302

Elements: 2√2, 4, 4√2, 6, 6√2, 12, 41, 32√2, 41√2, 64, 55√2, 78, 64√2, 96, 110, 96√2, 151, 206, 151√2.

Code: 2065 0 96 1514 151 151 1513 302 151 554 206 96 410 261 151 411 302 151 26 218 108 47 220 110 46 220 106 787 224 110 1103 302 0 123 218 96 62 224 102 63 224 96 967 0 96 960 96 96 644 160 32 643 224 32 324 192 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)