Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:224BS GHM

Order: 20

Horizontal side: 224 Vertical side: 224

Elements: 12, 12√2, 24, 18√2, 22√2, 23√2, 24√2, 38, 44, 46, 48, 50, 46√2, 68, 88, 90, 67√2, 68√2, 134, 156.

Code: 1565 0 68 1341 134 224 672 201 157 901 224 224 230 201 157 443 178 90 462 224 88 461 224 134 224 156 68 483 178 42 883 224 0 687 0 68 680 68 68 501 118 68 387 118 68 126 118 30 245 130 18 244 154 18 125 118 18 184 136 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)