Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:216AX GHM

Order: 19

Horizontal side: 216 Vertical side: 216

Elements: 2, 2√2, 12√2, 13√2, 24, 20√2, 22√2, 24√2, 25√2, 38, 44, 50, 44√2, 64, 86, 108, 86√2, 130, 108√2.

Code: 1305 0 86 1084 108 108 1083 216 108 224 130 86 200 152 108 641 216 108 20 132 88 21 134 88 132 147 75 381 172 88 442 216 44 867 0 86 860 86 86 244 110 62 243 134 62 250 147 75 124 122 50 501 172 50 443 216 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)