Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:45AA GHM

Order: 20

Horizontal side: 45 Vertical side: 45

Elements: 1√2, 2√2, 4, 3√2, 4√2, 6, 8, 9, 7√2, 11, 8√2, 12, 9√2, 11√2, 12√2, 18, 22, 24, 17√2, 18√2.

Code: 182 18 27 174 17 28 110 34 45 111 45 45 30 23 34 221 45 34 20 20 31 61 26 31 72 33 24 16 17 28 47 18 29 40 22 29 183 18 9 82 26 17 81 26 25 243 33 0 122 45 12 123 45 0 95 0 0 94 9 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)