Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:168AE GHM

Order: 20

Horizontal side: 168 Vertical side: 168

Elements: 4, 4√2, 5√2, 8, 10, 12, 12√2, 20, 20√2, 32, 42, 44, 60, 64, 47√2, 52√2, 74, 62√2, 64√2, 74√2.

Code: 745 0 94 744 74 94 443 148 124 207 148 168 206 148 148 122 160 136 123 160 124 85 160 128 45 160 124 44 164 124 646 104 64 626 42 62 607 104 124 472 47 47 421 42 94 327 42 94 645 104 0 105 42 52 54 47 47 520 52 52

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)