Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:160AY GHM

Order: 20

Horizontal side: 160 Vertical side: 160

Elements: 4, 12, 16, 12√2, 20, 22, 16√2, 24, 32, 23√2, 34, 44, 46, 48, 34√2, 46√2, 68, 57√2, 92, 80√2.

Code: 925 0 68 804 80 80 576 103 103 230 103 103 121 92 80 347 92 80 340 126 80 685 0 0 481 48 68 325 48 36 441 92 68 227 92 46 460 114 46 461 160 46 165 48 20 164 64 20 120 80 36 43 68 20 247 68 24 201 68 20

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)