Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:340AE GHM

Order: 20

Horizontal side: 340 Vertical side: 340

Elements: 11√2, 16, 16√2, 28, 32, 24√2, 28√2, 48, 56, 48√2, 78, 106, 78√2, 112, 134, 106√2, 156, 117√2, 128√2, 156√2.

Code: 1565 0 184 1564 156 184 280 312 340 281 340 340 240 284 312 561 340 312 480 260 288 481 308 288 325 308 256 165 308 240 164 324 240 1286 212 128 1343 212 106 1127 212 240 785 0 106 784 78 106 112 223 117 1170 223 117 1065 0 0 1064 106 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)