Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:100AR GHM

Order: 20

Horizontal side: 100 Vertical side: 100

Elements: 3, 4, 3√2, 6, 11√2, 16, 12√2, 20, 22, 16√2, 24, 25, 19√2, 28, 20√2, 28√2, 44, 36√2, 56, 50√2.

Code: 565 0 44 504 50 50 366 64 64 110 64 64 30 53 53 221 75 53 255 75 28 61 56 50 192 75 31 445 0 0 204 20 24 203 40 24 167 40 44 166 40 28 33 75 28 45 40 24 280 72 28 281 100 28 241 44 24 122 56 12

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)