Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:304AA GHM

Order: 19

Horizontal side: 304 Vertical side: 304

Elements: 11√2, 24, 28, 40, 32√2, 56, 40√2, 64, 56√2, 62√2, 90, 64√2, 118, 124, 90√2, 96√2, 146, 107√2, 124√2.

Code: 1245 0 180 1244 124 180 406 208 264 567 248 304 566 248 248 1463 208 118 405 208 224 245 248 224 642 272 160 641 272 224 322 304 192 966 208 96 902 90 90 624 62 118 281 90 118 1187 90 118 116 197 107 1070 197 107 903 90 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)