Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:136AL GHM

Order: 20

Horizontal side: 136 Vertical side: 136

Elements: 1√2, 2, 2√2, 4, 8, 8√2, 16, 12√2, 24, 24√2, 35, 37, 30√2, 33√2, 35√2, 36√2, 64, 66, 72, 68√2.

Code: 725 0 64 684 68 68 663 136 70 20 70 70 334 103 37 356 101 35 41 72 68 302 102 38 645 0 0 364 36 28 246 48 40 126 36 28 245 48 16 10 102 38 373 101 0 27 101 37 355 101 0 161 64 16 82 72 8 81 72 16

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)