Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:204AL GHM

Order: 20

Horizontal side: 204 Vertical side: 204

Elements: 1√2, 2, 2√2, 4, 5√2, 6√2, 7√2, 14, 13√2, 20, 36, 28√2, 36√2, 56, 76, 56√2, 92, 84√2, 92√2, 148.

Code: 1487 0 204 360 148 204 361 184 204 132 197 191 201 204 204 70 197 191 66 184 178 147 190 184 926 112 92 52 189 173 10 189 173 43 188 168 22 190 170 21 190 172 846 28 84 767 112 168 925 112 0 280 28 84 567 0 56 560 56 56

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)