Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:148AO GHM

Order: 20

Horizontal side: 148 Vertical side: 148

Elements: 3, 3√2, 6, 9, 9√2, 10√2, 20, 15√2, 20√2, 30, 24√2, 40, 30√2, 34√2, 54, 40√2, 60, 74, 88, 74√2.

Code: 887 0 148 400 88 148 401 128 148 202 148 128 201 148 148 543 148 74 30 48 108 31 51 108 97 51 108 96 51 99 242 84 84 344 94 74 150 45 105 61 51 105 300 30 90 301 60 90 100 84 84 740 74 74 741 148 74 607 0 60

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)