Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:254AI GHM

Order: 20

Horizontal side: 254 Vertical side: 254

Elements: 12, 12√2, 15√2, 30, 22√2, 30√2, 46, 60, 46√2, 68, 80, 82, 60√2, 90, 92, 104, 75√2, 82√2, 126, 104√2.

Code: 1045 0 150 1044 104 150 923 208 162 462 254 208 461 254 254 1263 254 82 120 116 162 121 128 162 807 128 162 752 75 75 601 60 150 302 90 120 681 128 150 303 90 90 602 150 60 154 75 75 903 90 0 224 150 60 820 172 82 821 254 82

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)