Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:178AH GHM

Order: 20

Horizontal side: 178 Vertical side: 178

Elements: 4√2, 7√2, 14, 16√2, 18√2, 22√2, 32, 36, 38, 44, 50, 38√2, 58, 64, 70, 76, 57√2, 60√2, 64√2, 70√2.

Code: 705 0 108 704 70 108 380 140 178 381 178 178 323 102 108 162 118 124 761 178 140 600 118 124 587 0 108 226 36 86 447 58 108 363 36 50 182 54 68 40 54 68 143 50 50 72 57 57 644 114 0 643 178 0 570 57 57 507 0 50

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)