Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:224AS GHM

Order: 20

Horizontal side: 224 Vertical side: 224

Elements: 4, 8√2, 12, 11√2, 16, 12√2, 20, 22, 16√2, 24, 24√2, 30√2, 52, 60, 82, 71√2, 112, 82√2, 142, 112√2.

Code: 1425 0 82 1124 112 112 1123 224 112 304 142 82 80 172 112 521 224 112 223 164 82 162 180 88 161 180 104 205 180 84 43 180 84 126 164 72 247 176 84 240 200 84 825 0 0 824 82 0 116 153 71 125 164 60 710 153 71 601 224 60

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)