Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:176AE GHM

Order: 20

Horizontal side: 176 Vertical side: 176

Elements: 6√2, 14√2, 24, 17√2, 28, 24√2, 34, 28√2, 31√2, 48, 34√2, 37√2, 42√2, 60, 48√2, 51√2, 74, 54√2, 60√2, 74√2.

Code: 745 0 102 744 74 102 146 134 162 287 148 176 286 148 148 420 134 162 240 92 120 241 116 120 607 116 120 606 116 60 512 51 51 374 37 65 316 37 65 482 116 48 481 116 96 62 122 54 540 122 54 170 51 51 340 34 34 341 68 34

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)