Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:218AL GHM

Order: 20

Horizontal side: 218 Vertical side: 218

Elements: 4√2, 8, 8√2, 12, 12√2, 24, 18√2, 30, 32, 28√2, 30√2, 31√2, 32√2, 62, 46√2, 62√2, 94, 93√2, 94√2, 156.

Code: 1567 0 218 320 156 218 321 188 218 302 218 188 301 218 218 946 124 94 936 31 93 462 170 140 284 152 158 46 176 182 87 180 186 86 180 178 243 176 158 122 188 170 123 188 158 184 170 140 945 124 0 310 31 93 627 0 62 620 62 62

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)