Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:256AD GHM

Order: 20

Horizontal side: 256 Vertical side: 256

Elements: 12, 12√2, 24, 17√2, 30, 34, 36, 34√2, 36√2, 60, 64, 68, 60√2, 94, 68√2, 81√2, 90√2, 132, 94√2, 98√2.

Code: 982 98 158 814 81 175 643 162 192 947 162 256 946 162 162 176 81 175 347 98 192 1323 132 60 902 222 102 301 162 192 340 222 102 680 188 68 681 256 68 607 0 60 600 60 60 364 96 24 363 132 24 241 120 24 122 132 12 121 132 24

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)