Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:157AA GHM

Order: 20

Horizontal side: 157 Vertical side: 157

Elements: 6, 6√2, 12, 9√2, 13, 16, 18, 16√2, 18√2, 32, 42, 32√2, 48, 40√2, 61, 64, 48√2, 77, 80, 109.

Code: 1097 0 157 773 109 80 487 109 157 486 109 109 425 109 67 326 0 48 647 32 80 803 96 0 402 136 40 131 109 80 184 127 49 183 145 49 67 145 67 60 151 67 127 145 61 613 157 0 94 136 40 325 0 16 165 0 0 164 16 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)