Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:176AF GHM

Order: 20

Horizontal side: 176 Vertical side: 176

Elements: 6, 10√2, 18, 14√2, 17√2, 18√2, 28, 34, 28√2, 48, 34√2, 42√2, 60, 66, 48√2, 51√2, 74, 58√2, 60√2, 74√2.

Code: 745 0 102 744 74 102 146 134 162 287 148 176 286 148 148 663 134 96 422 176 120 606 116 60 512 51 51 344 34 68 343 68 68 67 68 102 487 68 96 486 68 48 182 134 78 181 134 96 174 51 51 106 58 58 605 116 0 580 58 58

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)