Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:187AC GHM

Order: 20

Horizontal side: 187 Vertical side: 187

Elements: 16, 16√2, 31, 22√2, 32, 33, 42, 31√2, 44, 32√2, 46, 33√2, 44√2, 64, 66, 77, 79, 90, 66√2, 77√2.

Code: 797 0 187 326 47 155 647 79 187 226 121 165 447 143 187 446 143 143 423 121 123 662 187 99 166 31 139 325 47 123 316 0 108 165 31 123 465 31 77 901 121 123 315 0 77 663 187 33 777 0 77 770 77 77 334 154 0 333 187 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)