Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:204AE GHM

Order: 20

Horizontal side: 204 Vertical side: 204

Elements: 2, 2√2, 4, 4√2, 9√2, 18, 24, 18√2, 24√2, 28√2, 42, 50, 56, 51√2, 56√2, 84, 60√2, 102, 120, 102√2.

Code: 1205 0 84 1024 102 102 1023 204 102 184 120 84 240 138 102 241 162 102 427 162 102 516 153 51 845 0 0 564 56 28 563 112 28 45 112 80 44 116 80 25 112 78 24 114 78 507 112 78 183 162 60 600 144 60 94 153 51 284 84 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)