Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:158AB GHM

Order: 20

Horizontal side: 158 Vertical side: 158

Elements: 4√2, 8, 8√2, 13, 16, 14√2, 21, 17√2, 28, 20√2, 34, 28√2, 40, 56, 62, 45√2, 48√2, 68, 96, 79√2.

Code: 965 0 62 794 79 79 456 113 113 343 113 79 215 113 92 137 113 92 80 126 92 81 134 92 42 138 88 200 138 88 563 118 28 167 118 84 174 96 62 407 118 68 683 158 0 625 0 0 484 48 14 146 48 14 285 62 0 284 90 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)