Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:256AY GHM

Order: 20

Horizontal side: 256 Vertical side: 256

Elements: 16, 16√2, 17√2, 32, 28√2, 32√2, 50, 56, 60, 74, 56√2, 84, 60√2, 88, 98, 74√2, 108, 84√2, 91√2, 98√2.

Code: 1085 0 148 914 91 165 740 182 256 741 256 256 176 91 165 507 108 182 980 158 182 981 256 182 607 0 148 606 0 88 322 92 116 321 92 148 162 108 132 161 108 148 885 0 0 565 60 28 564 116 28 840 172 84 841 256 84 284 88 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)