Primitive Perfect Isosceles Right Triangled Square

Title: _r 19:216AC4of4 GHM

Order: 19

Horizontal side: 216 Vertical side: 216

Elements: 2, 2√2, 4, 3√2, 6, 16√2, 32, 32√2, 48, 54, 64, 48√2, 50√2, 54√2, 57√2, 102, 108, 114, 108√2.

Code: 1147 0 216 643 114 152 482 162 168 481 162 216 547 162 216 546 162 162 36 159 165 570 159 165 500 50 152 324 82 120 323 114 120 164 98 104 43 102 104 67 102 108 1080 108 108 1081 216 108 24 100 102 23 102 102 1027 0 102

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)