Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:114AF GHM

Order: 20

Horizontal side: 114 Vertical side: 114

Elements: 2√2, 4, 4√2, 8, 6√2, 9, 8√2, 12, 9√2, 14, 16, 16√2, 23, 32, 51, 53, 61, 63, 45√2, 53√2.

Code: 635 0 51 611 61 114 537 61 114 536 61 61 42 65 57 43 65 53 92 74 48 24 63 51 143 65 39 517 0 51 66 45 45 127 51 51 93 74 39 325 74 16 450 45 45 231 74 39 164 90 0 163 106 0 82 114 8 83 114 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)