Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:328BY GHM

Order: 20

Horizontal side: 328 Vertical side: 328

Elements: 2√2, 4, 4√2, 8, 7√2, 14, 10√2, 20, 22, 26, 34, 41√2, 82, 112, 82√2, 108√2, 112√2, 164, 216, 164√2.

Code: 2165 0 112 1644 164 164 1643 328 164 414 205 123 343 246 130 827 246 164 826 246 82 76 205 123 147 212 130 106 216 120 207 226 130 223 246 108 46 212 116 85 216 112 1125 0 0 1124 112 0 43 224 108 22 226 110 1080 220 108 261 246 108

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)