Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:368AA GHM

Order: 20

Horizontal side: 368 Vertical side: 368

Elements: 13√2, 26, 26√2, 32√2, 33√2, 39√2, 64, 78, 80, 94, 80√2, 128, 130, 94√2, 146, 111√2, 160, 162, 128√2, 144√2.

Code: 1467 0 368 940 146 368 941 240 368 1282 368 240 1281 368 368 136 39 261 267 52 274 266 52 248 1305 78 144 1621 240 274 390 39 261 1603 368 80 1112 111 111 781 78 222 334 111 111 1440 144 144 641 208 144 322 240 112 804 288 0 803 368 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)