Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:312BI GHM

Order: 20

Horizontal side: 312 Vertical side: 312

Elements: 3, 3√2, 6, 9, 9√2, 15√2, 18√2, 44, 44√2, 66, 88, 92, 66√2, 110, 88√2, 92√2, 154, 110√2, 158, 202.

Code: 2027 0 312 1583 202 154 1107 202 312 1106 202 202 182 220 184 156 205 169 922 312 92 36 202 166 65 205 163 35 202 163 97 202 163 90 211 163 446 0 110 885 44 66 884 132 66 1543 220 0 445 0 66 923 312 0 665 0 0 664 66 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)