Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:188AO4of8 GHM

Order: 20

Horizontal side: 188 Vertical side: 188

Elements: 3√2, 6, 6√2, 10, 12, 9√2, 12√2, 20, 16√2, 30, 32, 42, 52, 42√2, 52√2, 84, 94, 68√2, 104, 94√2.

Code: 1045 0 84 944 94 94 943 188 94 101 104 94 125 104 82 424 146 52 423 188 52 847 0 84 166 68 68 325 84 52 201 104 84 92 113 73 64 110 76 63 116 76 305 116 52 34 113 73 126 104 64 680 68 68 524 136 0 523 188 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)