Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:224AK GHM

Order: 20

Horizontal side: 224 Vertical side: 224

Elements: 2, 6√2, 12, 12√2, 13√2, 20, 22, 24, 26, 20√2, 24√2, 46, 46√2, 66, 92, 66√2, 79√2, 112, 132, 112√2.

Code: 1325 0 92 1124 112 112 1123 224 112 201 132 112 225 132 90 464 178 66 463 224 66 927 0 92 136 79 79 265 92 66 204 112 72 23 132 90 126 118 78 247 130 90 240 154 90 790 79 79 66 112 72 125 118 66 664 158 0 663 224 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)