Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:368AP GHM

Order: 20

Horizontal side: 368 Vertical side: 368

Elements: 16√2, 28, 32, 32√2, 39√2, 56, 64, 50√2, 78, 64√2, 100, 106, 78√2, 112, 84√2, 128, 134, 128√2, 145√2, 184√2.

Code: 1842 184 184 1454 145 223 1063 290 262 787 290 368 786 290 290 285 290 262 396 145 223 1347 184 262 500 318 262 840 268 212 1001 368 212 563 184 128 1280 128 128 1281 256 128 642 320 64 641 320 128 322 352 96 321 352 128 162 368 112 1123 368 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)