Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:176AW2of2 GHM

Order: 20

Horizontal side: 176 Vertical side: 176

Elements: 2, 2√2, 4, 4√2, 6, 7√2, 14, 10√2, 13√2, 20, 20√2, 24√2, 34, 54, 68, 54√2, 88, 68√2, 108, 88√2.

Code: 1085 0 68 884 88 88 883 176 88 204 108 68 76 121 81 145 128 74 244 152 64 343 176 54 130 121 81 61 134 74 45 134 70 44 138 70 203 142 54 102 152 64 25 134 68 24 136 68 685 0 0 684 68 0 540 122 54 541 176 54

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)