Primitive Perfect Isosceles Right Triangled Square

Title: _r 19:139AE4of4 GHM

Order: 19

Horizontal side: 139 Vertical side: 139

Elements: 5√2, 10, 14, 10√2, 14√2, 20, 15√2, 28, 20√2, 21√2, 28√2, 42, 35√2, 55, 56, 42√2, 48√2, 70, 97.

Code: 977 0 139 280 97 139 281 125 139 142 139 125 141 139 139 703 139 55 486 21 63 567 69 111 210 21 63 202 89 35 354 104 20 553 139 0 427 0 42 420 42 42 203 89 15 152 104 20 104 79 5 103 89 5 54 84 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)