Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:160BK GHM

Order: 20

Horizontal side: 160 Vertical side: 160

Elements: 12, 12√2, 18, 20, 15√2, 24, 18√2, 20√2, 30, 24√2, 40, 29√2, 30√2, 48, 40√2, 60, 45√2, 60√2, 100, 71√2.

Code: 1005 0 60 714 71 89 180 142 160 181 160 160 240 124 142 241 148 142 122 160 130 121 160 142 456 115 85 296 71 89 487 100 118 150 115 85 307 100 70 300 130 70 607 0 60 600 60 60 204 80 40 203 100 40 404 120 0 403 160 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)