Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:272AX GHM

Order: 20

Horizontal side: 272 Vertical side: 272

Elements: 5√2, 10, 12, 10√2, 12√2, 20, 25√2, 35√2, 50, 56, 45√2, 68, 56√2, 62√2, 68√2, 80√2, 124, 136, 148, 136√2.

Code: 1487 0 272 626 86 210 1247 148 272 1366 136 136 256 61 185 505 86 160 50 61 185 566 0 124 107 56 180 106 56 170 205 66 160 452 101 125 354 101 125 806 56 80 122 148 148 1365 136 0 565 0 68 125 56 68 687 0 68 680 68 68

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)