Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:204AA GHM

Order: 20

Horizontal side: 204 Vertical side: 204

Elements: 6, 19√2, 21√2, 25√2, 38, 28√2, 40, 42, 44, 50, 56, 40√2, 42√2, 78, 56√2, 80, 82, 63√2, 80√2, 82√2.

Code: 825 0 122 824 82 122 400 164 204 401 204 204 800 124 164 801 204 164 447 0 122 196 25 103 387 44 122 250 25 103 61 50 84 565 50 28 564 106 28 216 141 63 427 162 84 426 162 42 785 0 0 501 50 78 630 141 63 284 78 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)