Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:222BB GHM

Order: 19

Horizontal side: 222 Vertical side: 222

Elements: 8, 7√2, 8√2, 14, 14√2, 28, 41, 42, 45, 33√2, 49, 50, 45√2, 66, 78, 78√2, 111, 144, 111√2.

Code: 1445 0 78 1114 111 111 1113 222 111 334 144 78 413 177 70 452 222 66 451 222 111 787 0 78 780 78 78 501 128 78 85 128 70 84 136 70 425 128 28 491 177 70 663 222 0 281 156 28 142 170 14 141 170 28 72 177 21

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)