Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:100AL GHM

Order: 20

Horizontal side: 100 Vertical side: 100

Elements: 4, 4√2, 5√2, 8, 12, 16, 12√2, 15√2, 16√2, 24, 26, 19√2, 32, 24√2, 29√2, 42, 32√2, 34√2, 52, 42√2.

Code: 527 0 100 320 52 100 321 84 100 162 100 84 161 100 100 426 58 42 83 20 60 42 24 64 194 39 49 346 24 34 267 58 68 43 24 60 152 39 49 120 12 60 121 24 60 242 24 24 241 24 48 425 58 0 52 29 29 290 29 29

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)