Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:159AA GHM

Order: 20

Horizontal side: 159 Vertical side: 159

Elements: 4, 15, 16, 12√2, 20, 16√2, 24, 28, 20√2, 30, 28√2, 30√2, 43, 58, 43√2, 44√2, 73, 58√2, 86, 101.

Code: 1017 0 159 733 101 86 587 101 159 586 101 101 155 101 86 286 0 58 202 48 66 444 72 42 863 116 0 432 159 43 203 48 46 245 48 42 285 0 30 167 28 46 160 44 46 41 48 46 433 159 0 124 60 30 305 0 0 304 30 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)