Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:74AE GHM

Order: 20

Horizontal side: 74 Vertical side: 74

Elements: 8, 9, 10, 8√2, 9√2, 10√2, 18, 13√2, 19, 20, 21, 17√2, 26, 19√2, 27, 20√2, 21√2, 34, 26√2, 27√2.

Code: 347 0 74 210 34 74 211 55 74 197 55 74 196 55 55 105 55 45 136 0 40 267 13 53 260 39 53 84 47 45 83 55 45 181 65 45 92 74 36 202 20 20 93 74 27 174 30 10 270 47 27 271 74 27 203 20 0 102 30 10

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)