Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:216AN GHM

Order: 19

Horizontal side: 216 Vertical side: 216

Elements: 4, 5, 4√2, 6, 5√2, 8, 6√2, 9√2, 17√2, 34, 34√2, 57, 68, 74, 91, 108, 125, 91√2, 108√2.

Code: 1255 0 91 1084 108 108 1083 216 108 174 125 91 83 142 100 62 148 102 741 216 108 63 148 96 685 148 34 90 134 100 44 138 96 43 142 96 54 143 91 53 148 91 917 0 91 910 91 91 571 148 91 344 182 0 343 216 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)