Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:272AL GHM

Order: 20

Horizontal side: 272 Vertical side: 272

Elements: 2, 6, 18√2, 36, 29√2, 35√2, 64, 70, 50√2, 72, 74, 76, 64√2, 100, 72√2, 76√2, 86√2, 122, 100√2, 104√2.

Code: 1042 104 168 864 86 186 506 122 222 1007 172 272 1006 172 172 363 122 186 762 198 146 184 104 168 1223 122 64 763 198 70 745 198 72 27 198 72 720 200 72 721 272 72 67 122 70 356 93 35 707 128 70 647 0 64 640 64 64 294 93 35

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)