Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:205AE GHM

Order: 20

Horizontal side: 205 Vertical side: 205

Elements: 4, 12, 11√2, 16, 12√2, 20, 22, 16√2, 24, 20√2, 22√2, 39, 39√2, 61, 44√2, 61√2, 72√2, 83√2, 122, 144.

Code: 1447 0 205 1223 144 83 612 205 144 611 205 205 726 133 72 226 0 61 127 22 83 126 22 71 245 34 59 444 78 39 830 122 83 114 133 72 162 38 55 225 0 39 41 38 59 207 38 59 200 58 59 163 38 39 395 0 0 394 39 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)