Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:128AF GHM

Order: 20

Horizontal side: 128 Vertical side: 128

Elements: 4, 10√2, 12√2, 18, 20, 22, 24, 18√2, 22√2, 24√2, 36, 40, 31√2, 44, 35√2, 50, 40√2, 42√2, 44√2, 52√2.

Code: 522 52 76 424 42 86 226 62 106 447 84 128 446 84 84 203 62 86 352 97 71 104 52 76 503 62 36 310 97 71 43 66 36 227 66 40 400 88 40 401 128 40 120 12 36 361 48 36 182 66 18 181 66 36 247 0 24 240 24 24

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)