Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:216AM1of2 GHM

Order: 20

Horizontal side: 216 Vertical side: 216

Elements: 2, 2√2, 4, 4√2, 7, 7√2, 10, 12, 14, 10√2, 23√2, 39, 46, 46√2, 78, 92, 78√2, 85√2, 138, 108√2.

Code: 1385 0 78 1084 108 108 856 131 131 236 108 108 395 131 92 77 131 92 76 131 85 145 138 78 104 148 82 103 158 82 127 158 92 923 170 0 462 216 46 44 152 78 43 156 78 22 158 80 21 158 82 785 0 0 784 78 0 463 216 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)