Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:100AA GHM

Order: 20

Horizontal side: 100 Vertical side: 100

Elements: 3√2, 6, 6√2, 9√2, 12√2, 14√2, 17√2, 18√2, 28, 21√2, 30, 32, 34, 36, 38, 28√2, 30√2, 32√2, 34√2, 36√2.

Code: 365 0 64 364 36 64 280 72 100 281 100 100 120 44 72 94 53 63 66 56 66 212 83 51 381 100 72 36 53 63 65 56 60 322 32 32 184 18 46 146 18 46 302 62 30 301 62 60 170 83 51 340 66 34 341 100 34 323 32 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)