Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:176AI GHM

Order: 20

Horizontal side: 176 Vertical side: 176

Elements: 7√2, 14, 12√2, 16√2, 24, 28, 24√2, 28√2, 36√2, 51, 37√2, 56, 60, 44√2, 65, 72, 51√2, 74, 60√2, 74√2.

Code: 745 0 102 744 74 102 563 148 120 282 176 148 281 176 176 446 132 104 126 80 108 247 92 120 246 92 96 602 176 60 164 132 104 360 80 108 512 51 51 374 37 65 70 44 72 721 116 72 141 51 65 655 51 0 603 176 0 513 51 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)