Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:272AJ GHM

Order: 20

Horizontal side: 272 Vertical side: 272

Elements: 2, 6, 29√2, 35√2, 43√2, 64, 70, 50√2, 72, 74, 76, 86, 64√2, 100, 72√2, 76√2, 79√2, 86√2, 122, 100√2.

Code: 1005 0 172 1004 100 172 743 200 198 727 200 272 726 200 200 25 200 198 760 126 198 761 202 198 705 202 128 862 86 86 504 50 122 65 202 122 354 237 93 646 208 64 794 129 43 1223 208 0 292 237 93 863 86 0 432 129 43 645 208 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)