Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:156AT GHM

Order: 19

Horizontal side: 156 Vertical side: 156

Elements: 3, 4, 4√2, 8, 12, 16, 20, 15√2, 20√2, 30, 33, 40, 30√2, 48, 63, 78, 63√2, 93, 78√2.

Code: 935 0 63 784 78 78 783 156 78 154 93 63 123 108 66 85 108 70 481 156 78 45 108 66 44 112 66 206 96 50 405 116 30 33 96 63 167 96 66 637 0 63 630 63 63 331 96 63 205 96 30 304 126 0 303 156 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)