Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:236AH GHM

Order: 19

Horizontal side: 236 Vertical side: 236

Elements: 12, 12√2, 15√2, 24, 30, 36, 46, 36√2, 58, 60, 44√2, 58√2, 60√2, 88, 104, 74√2, 88√2, 89√2, 132.

Code: 892 89 147 744 74 162 446 104 192 887 148 236 886 148 148 303 104 162 1325 104 60 154 89 147 1043 104 58 365 104 24 364 140 24 600 176 60 601 236 60 587 0 58 580 58 58 461 104 58 127 104 24 126 104 12 247 116 24

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)