Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:100AP GHM

Order: 20

Horizontal side: 100 Vertical side: 100

Elements: 1, 4, 4√2, 5√2, 8, 10, 11, 8√2, 12, 10√2, 16, 20, 16√2, 24, 20√2, 45, 50, 55, 45√2, 50√2.

Code: 555 0 45 504 50 50 503 100 50 54 55 45 46 56 46 87 60 50 86 60 42 165 68 34 164 84 34 206 80 30 13 56 45 125 56 34 457 0 45 450 45 45 111 56 45 241 80 34 47 80 34 205 80 10 104 90 0 103 100 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)