Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:191AA GHM

Order: 20

Horizontal side: 191 Vertical side: 191

Elements: 2√2, 8√2, 12, 10√2, 16, 12√2, 20, 28, 25√2, 44, 47, 50, 47√2, 50√2, 72, 91, 94, 69√2, 72√2, 75√2.

Code: 917 0 191 750 91 191 504 141 141 503 191 141 254 166 116 943 191 47 163 16 100 127 16 116 126 16 104 445 28 72 694 97 47 22 18 102 100 18 102 285 0 72 84 8 92 201 28 92 727 0 72 720 72 72 474 144 0 473 191 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)