Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:112BC GHM

Order: 20

Horizontal side: 112 Vertical side: 112

Elements: 4, 8√2, 12, 11√2, 16, 12√2, 20, 15√2, 22, 16√2, 24, 30, 24√2, 26√2, 41, 30√2, 52, 41√2, 60, 71.

Code: 715 0 41 601 60 112 242 84 88 521 112 112 243 84 64 205 84 68 47 84 68 160 88 68 161 104 68 82 112 60 125 60 52 124 72 52 306 82 30 114 71 41 266 56 26 227 82 52 417 0 41 410 41 41 154 56 26 305 82 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)