Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:242AW1of8 GHM

Order: 20

Horizontal side: 242 Vertical side: 242

Elements: 6√2, 12, 12√2, 21, 24, 18√2, 21√2, 36, 40, 42, 40√2, 42√2, 61, 80, 101, 80√2, 120, 122, 141, 101√2.

Code: 1415 0 101 1201 120 242 182 138 224 1221 242 242 126 126 212 245 138 200 66 120 206 125 126 200 422 162 164 361 162 200 802 242 120 423 162 122 214 141 101 213 162 101 803 242 40 1017 0 101 1010 101 101 611 162 101 404 202 0 403 242 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)