Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:456AC GHM

Order: 20

Horizontal side: 456 Vertical side: 456

Elements: 8, 8√2, 16, 24, 22√2, 24√2, 44, 48, 48√2, 88, 66√2, 96, 81√2, 162, 176, 125√2, 206, 250, 184√2, 228√2.

Code: 2505 0 206 2284 228 228 1846 272 272 443 272 228 1765 272 96 224 250 206 666 206 162 2065 0 0 1254 125 81 816 125 81 1625 206 0 961 368 96 482 416 48 481 416 96 242 440 72 241 440 96 87 440 96 80 448 96 167 440 88 883 456 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)