Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:100AO GHM

Order: 20

Horizontal side: 100 Vertical side: 100

Elements: 1, 4√2, 8, 6√2, 10, 8√2, 12, 10√2, 16, 20, 15√2, 16√2, 29, 30, 40, 30√2, 45, 35√2, 55, 50√2.

Code: 555 0 45 504 50 50 403 100 60 46 56 56 87 60 60 86 60 52 165 68 44 164 84 44 306 70 30 66 50 50 125 56 44 457 0 45 100 45 45 101 55 45 15 55 44 297 55 44 350 35 35 201 55 35 156 55 15 305 70 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)