Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:160BN GHM

Order: 20

Horizontal side: 160 Vertical side: 160

Elements: 1√2, 12, 12√2, 18, 20, 15√2, 24, 18√2, 20√2, 30, 24√2, 40, 30√2, 48, 40√2, 41√2, 45√2, 80, 100, 80√2.

Code: 1005 0 60 804 80 80 803 160 80 204 100 60 203 120 60 407 120 80 406 120 40 302 30 30 454 45 15 120 90 60 121 102 60 182 120 42 181 120 60 483 78 0 242 102 24 241 102 48 16 119 41 410 119 41 303 30 0 152 45 15

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)