Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:296AF GHM

Order: 20

Horizontal side: 296 Vertical side: 296

Elements: 9, 12√2, 24, 32, 41, 32√2, 48, 50, 37√2, 61, 64, 48√2, 74, 96, 74√2, 111, 87√2, 148, 124√2, 148√2.

Code: 1485 0 148 1484 148 148 1246 172 172 243 172 148 122 184 160 326 152 128 645 184 96 742 74 74 1111 111 148 617 111 148 413 152 87 325 152 96 95 152 87 961 248 96 482 296 48 507 111 87 870 161 87 743 74 0 372 111 37 483 296 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)