Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:112AA GHM

Order: 20

Horizontal side: 112 Vertical side: 112

Elements: 6, 6√2, 10, 9√2, 16, 18, 14√2, 20, 22, 16√2, 28, 20√2, 22√2, 36, 38, 36√2, 37√2, 38√2, 46√2, 48√2.

Code: 462 46 66 374 37 75 283 74 84 387 74 112 386 74 74 96 37 75 187 46 84 480 64 84 101 74 84 160 16 36 161 32 36 225 32 14 224 54 14 360 76 36 361 112 36 207 0 20 200 20 20 64 26 14 63 32 14 144 40 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)