Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:236AT GHM

Order: 19

Horizontal side: 236 Vertical side: 236

Elements: 10√2, 20, 16√2, 20√2, 32, 40, 32√2, 48, 35√2, 54, 40√2, 64, 70, 54√2, 67√2, 102, 118, 134, 118√2.

Code: 1345 0 102 1184 118 118 1183 236 118 324 150 86 483 182 70 542 236 64 541 236 118 1025 0 0 674 67 35 323 134 70 162 150 86 356 67 35 705 102 0 404 142 30 403 182 30 643 236 0 204 162 10 203 182 10 104 172 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)