Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:340AO GHM

Order: 20

Horizontal side: 340 Vertical side: 340

Elements: 30, 32, 25√2, 32√2, 48, 50, 64, 48√2, 50√2, 60√2, 64√2, 75√2, 112, 120, 128, 130, 160, 120√2, 180, 130√2.

Code: 1807 0 340 1206 60 220 1127 180 340 480 292 340 481 340 340 640 244 292 641 308 292 322 340 260 321 340 292 1306 210 130 1287 180 228 606 0 160 1205 60 100 1605 0 0 303 210 100 1305 210 0 754 135 25 506 160 50 256 135 25 505 160 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)