Primitive Perfect Isosceles Right Triangled Square

Title: __ 18:190AC1of2 GHM

Order: 18

Horizontal side: 190 Vertical side: 190

Elements: 5√2, 10, 10√2, 20, 15√2, 24√2, 44, 46, 48, 50, 46√2, 48√2, 70, 50√2, 94, 96, 70√2, 120.

Code: 1205 0 70 961 96 190 482 144 142 941 190 190 483 144 94 462 190 96 463 190 50 244 120 70 443 144 50 707 0 70 700 70 70 154 85 55 106 90 60 207 100 70 56 85 55 105 90 50 504 140 0 503 190 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)