Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:270AW1of2 GHM

Order: 20

Horizontal side: 270 Vertical side: 270

Elements: 6, 5√2, 6√2, 8√2, 12, 16, 12√2, 18, 13√2, 34, 42, 38√2, 42√2, 76, 76√2, 110, 118, 114√2, 118√2, 194.

Code: 1947 0 270 420 194 270 421 236 270 122 248 258 341 270 270 123 248 246 62 254 252 63 254 246 165 254 236 187 236 246 56 249 241 130 249 241 84 262 228 1186 152 118 1146 38 114 1107 152 228 1185 152 0 380 38 114 767 0 76 760 76 76

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)