Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:188AG GHM

Order: 20

Horizontal side: 188 Vertical side: 188

Elements: 2, 13√2, 26, 20√2, 22√2, 26√2, 38, 40, 42, 34√2, 52, 38√2, 42√2, 68, 52√2, 76, 60√2, 86, 68√2, 73√2.

Code: 732 73 115 604 60 128 346 86 154 687 120 188 686 120 120 263 86 128 765 86 78 134 73 115 863 86 42 385 86 40 384 124 40 260 162 78 520 136 52 521 188 52 427 0 42 420 42 42 224 64 20 23 86 40 206 64 20 407 84 40

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)