Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:186BG GHM

Order: 20

Horizontal side: 186 Vertical side: 186

Elements: 4, 4√2, 8, 8√2, 16, 14√2, 15√2, 28, 21√2, 30, 28√2, 42, 51, 42√2, 72, 51√2, 57√2, 93, 114, 93√2.

Code: 1145 0 72 934 93 93 933 186 93 214 114 72 510 135 93 511 186 93 725 0 0 574 57 15 40 84 42 41 88 42 285 88 14 284 116 14 420 144 42 421 186 42 80 80 38 81 88 38 156 57 15 305 72 0 161 88 30 144 102 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)