Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:226AA GHM

Order: 20

Horizontal side: 226 Vertical side: 226

Elements: 6, 6√2, 12, 11√2, 18, 18√2, 36, 44, 36√2, 58, 44√2, 66, 80, 58√2, 88, 66√2, 94, 80√2, 88√2, 91√2.

Code: 947 0 226 880 94 226 881 182 226 442 226 182 441 226 226 916 135 91 60 6 138 61 12 138 187 12 138 186 12 120 367 30 138 366 30 102 585 66 80 584 124 80 662 66 66 121 12 132 110 135 91 807 66 80 800 146 80 663 66 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)