Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:114AM GHM

Order: 20

Horizontal side: 114 Vertical side: 114

Elements: 1, 1√2, 2, 3, 3√2, 6, 12, 16, 12√2, 16√2, 24, 32, 36, 30√2, 32√2, 48, 54, 60, 66, 49√2.

Code: 667 0 114 363 66 78 487 66 114 603 114 54 300 30 78 241 54 78 122 66 66 121 66 78 61 60 54 32 63 51 541 114 54 33 63 48 25 63 49 15 63 48 14 64 48 490 65 49 325 0 16 324 32 16 165 0 0 164 16 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)