Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:148AA GHM

Order: 20

Horizontal side: 148 Vertical side: 148

Elements: 7√2, 14, 16, 18, 20, 16√2, 18√2, 36, 26√2, 38, 42, 52, 38√2, 54, 40√2, 42√2, 47√2, 68, 52√2, 54√2.

Code: 687 0 148 420 68 148 421 110 148 387 110 148 386 110 110 205 110 90 266 0 80 527 26 106 520 78 106 164 94 90 163 110 90 361 130 90 182 148 72 402 40 40 183 148 54 141 40 54 72 47 47 544 94 0 543 148 0 470 47 47

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)