Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:168AH GHM

Order: 20

Horizontal side: 168 Vertical side: 168

Elements: 1√2, 4√2, 8, 8√2, 12, 14, 16, 12√2, 14√2, 15√2, 24, 26, 48, 54, 48√2, 54√2, 84, 60√2, 96, 84√2.

Code: 845 0 84 844 84 84 606 108 108 243 108 84 122 120 96 963 120 0 482 168 48 545 0 30 544 54 30 483 168 0 152 15 15 144 14 16 143 28 16 267 28 30 14 15 15 163 16 0 82 24 8 121 28 16 83 24 0 42 28 4

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)