Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:225AE GHM

Order: 20

Horizontal side: 225 Vertical side: 225

Elements: 6, 6√2, 9, 10, 12, 9√2, 10√2, 12√2, 20, 21, 24, 55, 75, 55√2, 85, 95, 75√2, 85√2, 140, 150.

Code: 1505 0 75 1401 140 225 857 140 225 856 140 140 245 140 116 215 140 95 124 152 104 123 164 104 62 170 110 63 170 104 552 225 55 94 161 95 93 170 95 107 140 95 106 140 85 207 150 95 953 170 0 755 0 0 754 75 0 553 225 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)