Primitive Perfect Isosceles Right Triangled Square

Title: __ 18:190AA2of2 GHM

Order: 18

Horizontal side: 190 Vertical side: 190

Elements: 5√2, 10, 10√2, 20, 15√2, 24√2, 25√2, 44, 46, 48, 50, 46√2, 48√2, 50√2, 94, 96, 70√2, 95√2.

Code: 965 0 94 954 95 95 706 120 120 256 95 95 205 120 100 152 135 85 104 130 90 103 140 90 502 190 50 945 0 0 484 48 46 483 96 46 242 120 70 54 135 85 443 140 46 503 190 0 464 94 0 463 140 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)