Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:102AN GHM

Order: 20

Horizontal side: 102 Vertical side: 102

Elements: 3, 3√2, 6, 5√2, 9, 10, 9√2, 10√2, 18, 16√2, 18√2, 19√2, 32, 36, 38, 32√2, 33√2, 48, 35√2, 51√2.

Code: 512 51 51 361 36 102 182 54 84 334 69 69 383 102 64 183 54 66 102 64 74 103 64 64 52 69 69 94 45 57 93 54 57 487 54 64 326 70 32 61 51 57 32 54 54 31 54 57 196 35 35 350 35 35 166 54 16 325 70 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)