Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:113AC GHM

Order: 20

Horizontal side: 113 Vertical side: 113

Elements: 4√2, 10, 14, 10√2, 17, 14√2, 20, 15√2, 28, 20√2, 21√2, 30, 31, 25√2, 40, 30√2, 48, 50, 53, 83.

Code: 837 0 113 200 83 113 201 103 113 102 113 103 101 113 113 503 113 53 483 63 45 407 63 93 42 67 49 254 88 28 533 113 0 210 67 49 150 15 45 311 46 45 177 46 45 307 0 30 300 30 30 147 46 28 146 46 14 287 60 28

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)