Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:364AB GHM

Order: 20

Horizontal side: 364 Vertical side: 364

Elements: 9, 9√2, 18, 18√2, 27√2, 31√2, 60, 62, 61√2, 62√2, 120, 121, 122, 93√2, 150, 120√2, 121√2, 122√2, 181, 183.

Code: 1225 0 242 1224 122 242 1833 244 181 1207 244 364 1206 244 244 272 271 217 1212 121 121 614 61 181 186 253 199 932 364 124 96 244 190 185 253 181 95 244 181 601 121 181 1815 121 0 1501 271 181 626 302 62 1213 121 0 316 271 31 625 302 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)