Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:224AI GHM

Order: 20

Horizontal side: 224 Vertical side: 224

Elements: 2√2, 4, 4√2, 8, 8√2, 10√2, 16, 20, 16√2, 40, 52, 40√2, 41√2, 80, 82, 61√2, 102, 122, 92√2, 112√2.

Code: 1225 0 102 1124 112 112 926 132 132 203 132 112 525 132 80 104 122 102 166 116 96 1025 0 0 614 61 41 86 108 88 165 116 80 46 104 84 85 108 80 26 102 82 45 104 80 416 61 41 825 102 0 801 184 80 402 224 40 403 224 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)